sqrt(r^2-x^2)

Time bar (total: 4.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze19.0ms (0.5%)

Memory
7.4MiB live, 7.4MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%0%100%0%0%0%0
0%0%0%100%0%0%0%1
0%0%0%100%0%0%0%2
33.3%0%0%100%0%0%0%3
33.3%0%0%100%0%0%0%4
60%0%0%100%0%0%0%5
60%0%0%100%0%0%0%6
77.8%0%0%100%0%0%0%7
77.8%0%0%100%0%0%0%8
88.2%0%0%100%0%0%0%9
88.2%0%0%100%0%0%0%10
93.9%0%0%100%0%0%0%11
93.9%0%0%100%0%0%0%12
Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.2s (30.9%)

Memory
28.8MiB live, 715.8MiB allocated
Samples
793.0ms8 256×0valid
21.0ms267×0invalid
Precisions
Click to see histograms. Total time spent on operations: 542.0ms
ival-pow2: 241.0ms (44.4% of total)
ival-<=: 100.0ms (18.4% of total)
ival-sqrt: 91.0ms (16.8% of total)
ival-and: 50.0ms (9.2% of total)
ival-sub: 39.0ms (7.2% of total)
exact: 18.0ms (3.3% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain79.0ms (2%)

Memory
45.1MiB live, 45.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
00-0-(pow.f64 r #s(literal 2 binary64))
00-0-(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
00-0-r
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
32.0ms512×0valid
Compiler

Compiled 60 to 25 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-pow2: 10.0ms (58.7% of total)
ival-sqrt: 4.0ms (23.5% of total)
ival-sub: 2.0ms (11.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess435.0ms (10.9%)

Memory
-30.5MiB live, 47.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01746
13742
28642
321442
441042
593242
6135242
7201642
8289242
9369142
10415742
11426142
12430742
13432542
14658742
15729042
16793442
078
0118
1158
2278
3388
4738
51588
64078
78668
817178
927438
1039808
1144938
1246978
1348498
1449278
1549278
1659388
1761068
1862748
1963588
2064428
2164428
2267788
2368628
2468628
2568628
089268
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Outputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
Symmetry

(abs x)

(abs r)

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.7%
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify315.0ms (7.9%)

Memory
40.2MiB live, 40.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(pow.f64 x #s(literal 2 binary64))
cost-diff0
(pow.f64 r #s(literal 2 binary64))
cost-diff0
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0724
01124
11524
22724
33824
47324
515824
640724
786624
8171724
9274324
10398024
11449324
12469724
13484924
14492724
15492724
16593824
17610624
18627424
19635824
20644224
21644224
22677824
23686224
24686224
25686224
0892624
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 r #s(literal 2 binary64))
r
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
x
Outputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (-.f64 r x) (+.f64 x r))
(pow.f64 r #s(literal 2 binary64))
(*.f64 r r)
r
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
x

localize21.0ms (0.5%)

Memory
8.3MiB live, 8.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(pow.f64 x #s(literal 2 binary64))
accuracy0.0
(pow.f64 r #s(literal 2 binary64))
accuracy0.09375
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
accuracy0.3241299997011715
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Samples
16.0ms256×0valid
Compiler

Compiled 26 to 9 computations (65.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-pow2: 5.0ms (60.6% of total)
ival-sqrt: 2.0ms (24.3% of total)
ival-sub: 1.0ms (12.1% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series96.0ms (2.4%)

Memory
-118.0MiB live, 2.6MiB allocated
Counts
4 → 29
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 r #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
Outputs
(* x (sqrt -1))
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(* -1 (pow x 2))
(- (pow r 2) (pow x 2))
(pow r 2)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(* -1 r)
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4)))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(+ r (* -1/2 (/ (pow x 2) r)))
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(+ r (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow r 5))) (* 1/8 (/ 1 (pow r 3))))) (* 1/2 (/ 1 r)))))
(+ (* -1 (pow x 2)) (pow r 2))
(pow x 2)
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
Calls

6 calls:

TimeVariablePointExpression
61.0ms
x
@-inf
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))
31.0ms
x
@inf
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))
1.0ms
r
@0
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))
1.0ms
r
@inf
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))
1.0ms
x
@0
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))

simplify173.0ms (4.3%)

Memory
47.6MiB live, 47.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119537
1332537
21153524
34633506
08289471
Stop Event
1×iter limit
1×node limit
Counts
29 → 28
Calls
Call 1
Inputs
(* x (sqrt -1))
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(* -1 (pow x 2))
(- (pow r 2) (pow x 2))
(pow r 2)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(* -1 r)
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4)))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(+ r (* -1/2 (/ (pow x 2) r)))
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(+ r (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow r 5))) (* 1/8 (/ 1 (pow r 3))))) (* 1/2 (/ 1 r)))))
(+ (* -1 (pow x 2)) (pow r 2))
(pow x 2)
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
Outputs
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 r r)) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) r) (/.f64 r (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(- (pow r 2) (pow x 2))
(*.f64 (-.f64 r x) (+.f64 x r))
(pow r 2)
(*.f64 r r)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(fma.f64 (*.f64 (/.f64 (*.f64 x x) r) #s(literal -1/2 binary64)) #s(literal 1 binary64) r)
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) r) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) r) #s(literal -1/2 binary64)) #s(literal 1 binary64) r))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 r #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x r)) (/.f64 x r) #s(literal 1 binary64)))) r)
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(*.f64 (-.f64 r x) (+.f64 x r))
(* -1 r)
(neg.f64 r)
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(fma.f64 (*.f64 (/.f64 (*.f64 x x) r) #s(literal -1/2 binary64)) #s(literal -1 binary64) (neg.f64 r))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4)))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) r) (/.f64 (*.f64 x x) r) #s(literal -1 binary64))) r)
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 r #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) r) (/.f64 (*.f64 x x) r) #s(literal -1 binary64)))) r)
(+ r (* -1/2 (/ (pow x 2) r)))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x) x (/.f64 #s(literal -1/2 binary64) r)) (*.f64 x x) r)
(+ r (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow r 5))) (* 1/8 (/ 1 (pow r 3))))) (* 1/2 (/ 1 r)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) x) (/.f64 x (pow.f64 r #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal -1/2 binary64) r)) (*.f64 x x) r)
(+ (* -1 (pow x 2)) (pow r 2))
(*.f64 (-.f64 r x) (+.f64 x r))
(pow x 2)
(*.f64 x x)
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (fma.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(neg.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
(neg.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) r) (/.f64 r x) (*.f64 (fma.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)))

rewrite201.0ms (5%)

Memory
-28.5MiB live, 55.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721
01121
14221
224321
3215821
0924921
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 285
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 r #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 r #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x r) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 r #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 r #s(literal 4 binary64))) (pow.f64 r #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x r) #s(literal 2 binary64))) (pow.f64 r #s(literal 4 binary64)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 x r) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 r x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 r #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x r) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 r #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 r #s(literal 4 binary64))) (pow.f64 r #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x r) #s(literal 2 binary64))) (pow.f64 r #s(literal 4 binary64)))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 x x (*.f64 r r))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 x x (*.f64 r r))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(*.f64 (sqrt.f64 (+.f64 x r)) (sqrt.f64 (-.f64 r x)))
(*.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 x r) (sqrt.f64 (/.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (fma.f64 x x (*.f64 r r)))))
(*.f64 (hypot.f64 x r) (sqrt.f64 (*.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64)))))
(*.f64 (hypot.f64 x r) (pow.f64 (/.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (fma.f64 x x (*.f64 r r))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 x r) (pow.f64 (*.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (sqrt.f64 (/.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (pow.f64 (/.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (pow.f64 (*.f64 (*.f64 (-.f64 r x) (+.f64 x r)) (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (neg.f64 (neg.f64 (hypot.f64 x r))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 x r))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64)))) (hypot.f64 (*.f64 x x) (*.f64 r r)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 r #s(literal 8 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 x r) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 r #s(literal 12 binary64)) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 x x (*.f64 r r))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) (fma.f64 x x (*.f64 r r)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 r #s(literal 8 binary64))) (fma.f64 x x (*.f64 r r)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x r) #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 r #s(literal 12 binary64))) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 r #s(literal 4 binary64)) (fma.f64 x x (*.f64 r r))) (*.f64 (fma.f64 x x (*.f64 r r)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (*.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) x) (*.f64 r r))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (hypot.f64 x r))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))))
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(+.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x (*.f64 r r)) (*.f64 x x) (pow.f64 r #s(literal 4 binary64))))))
(+.f64 (*.f64 (neg.f64 x) x) (*.f64 r r))
(+.f64 (*.f64 r r) (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 (-.f64 r x) (+.f64 x r)))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (*.f64 (-.f64 r x) (+.f64 x r))))
(*.f64 (pow.f64 (pow.f64 r #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 r #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 r #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 r))
(*.f64 (pow.f64 r #s(literal 3/2 binary64)) (sqrt.f64 r))
(*.f64 (sqrt.f64 r) (pow.f64 (pow.f64 r #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 r) (pow.f64 r #s(literal 3/2 binary64)))
(*.f64 r r)
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 r) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 r))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 r))
(pow.f64 (sqrt.f64 r) #s(literal 4 binary64))
(pow.f64 (pow.f64 r #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 r r) #s(literal 1 binary64))
(pow.f64 r #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 r)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 r)))
(exp.f64 (*.f64 (log.f64 r) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval38.0ms (1%)

Memory
30.1MiB live, 30.1MiB allocated
Compiler

Compiled 9 210 to 1 152 computations (87.5% saved)

prune8.0ms (0.2%)

Memory
14.4MiB live, 14.4MiB allocated
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3019310
Fresh000
Picked101
Done000
Total3029311
Accuracy
100.0%
Counts
311 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)) #s(literal 1 binary64))))
▶99.5%
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
99.7%
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
▶99.8%
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
▶99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
99.8%
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
99.6%
(sqrt.f64 #s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))))
▶79.3%
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
▶1.6%
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
Compiler

Compiled 216 to 162 computations (25% saved)

simplify149.0ms (3.7%)

Memory
-48.0MiB live, 29.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (-.f64 r x) (+.f64 x r))
cost-diff0
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
cost-diff4
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
cost-diff0
(sqrt.f64 (+.f64 x r))
cost-diff0
(-.f64 r x)
cost-diff0
(sqrt.f64 (-.f64 r x))
cost-diff0
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
cost-diff0
(/.f64 #s(literal -1/2 binary64) r)
cost-diff0
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
cost-diff0
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
cost-diff0
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
cost-diff0
(neg.f64 r)
cost-diff0
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 (neg.f64 x) x)
cost-diff0
(fma.f64 r r (*.f64 (neg.f64 x) x))
cost-diff0
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029147
048139
177139
2122139
3249139
4500139
5935139
62280139
74534139
87501139
08134139
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(fma.f64 r r (*.f64 (neg.f64 x) x))
r
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
r
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
(/.f64 #s(literal -1/2 binary64) r)
#s(literal -1/2 binary64)
r
x
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(sqrt.f64 (-.f64 r x))
(-.f64 r x)
r
x
(sqrt.f64 (+.f64 x r))
(+.f64 x r)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
(*.f64 (-.f64 r x) (+.f64 x r))
(-.f64 r x)
r
x
(+.f64 x r)
#s(literal -1 binary64)
Outputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(fma.f64 r r (*.f64 (neg.f64 x) x))
(fma.f64 (neg.f64 x) x (*.f64 r r))
r
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
r
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
(/.f64 #s(literal -1/2 binary64) r)
#s(literal -1/2 binary64)
r
x
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(*.f64 (sqrt.f64 (+.f64 x r)) (sqrt.f64 (-.f64 r x)))
(sqrt.f64 (-.f64 r x))
(-.f64 r x)
r
x
(sqrt.f64 (+.f64 x r))
(+.f64 x r)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
(fma.f64 (neg.f64 x) x (*.f64 r r))
#s(literal 1 binary64)
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
(pow.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)) #s(literal -1 binary64))
(*.f64 (-.f64 r x) (+.f64 x r))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(-.f64 r x)
r
x
(+.f64 x r)
#s(literal -1 binary64)

localize70.0ms (1.8%)

Memory
28.3MiB live, 28.3MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.0546875
(*.f64 (-.f64 r x) (+.f64 x r))
accuracy0.09375
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
accuracy0.27734375
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
accuracy0.31640625
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
accuracy0.0
(+.f64 x r)
accuracy0.1171875
(sqrt.f64 (+.f64 x r))
accuracy0.12109375
(sqrt.f64 (-.f64 r x))
accuracy0.328125
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
accuracy0.0
(/.f64 #s(literal -1/2 binary64) r)
accuracy0.00390625
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
accuracy0.29296875
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
accuracy13.276274613447066
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
accuracy0.0
(neg.f64 r)
accuracy62.98997936107201
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
accuracy0.0
(*.f64 (neg.f64 x) x)
accuracy0.0
(neg.f64 x)
accuracy0.033535009768442016
(fma.f64 r r (*.f64 (neg.f64 x) x))
accuracy0.09375
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
Samples
52.0ms256×0valid
Compiler

Compiled 140 to 30 computations (78.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 9.0ms (25% of total)
ival-sqrt: 8.0ms (22.2% of total)
ival-pow2: 4.0ms (11.1% of total)
ival-div: 3.0ms (8.3% of total)
ival-add: 3.0ms (8.3% of total)
ival-pow: 3.0ms (8.3% of total)
ival-sub: 2.0ms (5.6% of total)
ival-neg: 2.0ms (5.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series29.0ms (0.7%)

Memory
11.5MiB live, 11.5MiB allocated
Counts
19 → 137
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(fma.f64 r r (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
(/.f64 #s(literal -1/2 binary64) r)
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(sqrt.f64 (-.f64 r x))
(-.f64 r x)
(sqrt.f64 (+.f64 x r))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
(*.f64 (-.f64 r x) (+.f64 x r))
(+.f64 x r)
Outputs
(* x (sqrt -1))
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (pow r 2))
(* -1 r)
(* -1/2 (/ (pow x 2) r))
(/ (+ (* -1/2 (pow x 2)) (pow r 2)) r)
(* -1/2 (/ x r))
(/ -1/2 r)
(+ (* 1/2 (/ (* r (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* r (+ (* 1/2 (/ (* r (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))) (* x (sqrt -1)))
(+ (* r (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* r (+ (* -1/4 (/ (* r (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))) (* x (sqrt -1)))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 x)))) (* (sqrt x) (sqrt -1)))
(+ (* r (+ (* -1/8 (* (/ r (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 3))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* r (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* r (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ r (pow (sqrt -1) 5)) (sqrt (/ 1 (pow x 5))))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(- r x)
(sqrt x)
(+ (sqrt x) (* 1/2 (* r (sqrt (/ 1 x)))))
(+ (sqrt x) (* r (+ (* -1/8 (* r (sqrt (/ 1 (pow x 3))))) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* r (+ (* 1/2 (sqrt (/ 1 x))) (* r (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* r (sqrt (/ 1 (pow x 5))))))))))
(+ (* -1 (pow x 2)) (* r (+ x (* -1 x))))
(+ (* -1 (pow x 2)) (* r (+ r (+ x (* -1 x)))))
(/ -1 (pow x 2))
(- (* -1 (/ (pow r 2) (pow x 4))) (/ 1 (pow x 2)))
(- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 6))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(- (* (pow r 2) (- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
x
(+ r x)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(pow r 2)
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (* 1/2 (/ (+ x (* -1 x)) r))))
(* r (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2))))))
(* r (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow r 3))) (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2)))))))
(sqrt r)
(* r (+ (sqrt (/ 1 r)) (* -1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* -1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3)))))))
(* r (+ 1 (* -1 (/ x r))))
(* r (+ (sqrt (/ 1 r)) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))))
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (/ x r))))
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (/ x r)))))
(/ 1 (pow r 2))
(/ (+ 1 (* -1 (/ (+ x (* -1 x)) r))) (pow r 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))) (pow r 2)))) (+ (* -1 (/ x r)) (/ x r))) (pow r 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ x (* -1 x)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))))) (* (pow x 2) (+ x (* -1 x)))) (pow r 3)))) (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow r 2))) (/ x r))))) (pow r 2))
(* r (+ 1 (/ x r)))
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4)))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(* -1 (* r (- (* 1/2 (/ (pow x 2) (pow r 2))) 1)))
(* -1 (* r (pow (sqrt -1) 2)))
(* -1 (* r (+ (* -1/2 (/ (+ x (* -1 x)) r)) (pow (sqrt -1) 2))))
(* -1 (* r (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) r)) (* 1/2 (+ x (* -1 x)))) r)) (pow (sqrt -1) 2))))
(* -1 (* r (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* r (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) r)) (* 1/2 (+ x (* -1 x)))) r)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt r) (pow (sqrt -1) 2)))
(* -1 (* r (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (* (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2))))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (* (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (* (pow x 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))))
(* -1 (* r (- (/ x r) 1)))
(* -1 (* r (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (/ (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2))))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (/ (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (/ (pow x 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))))
(* (pow r 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) r)) r))))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow x 2) r)) (* -1 (/ (pow (+ x (* -1 x)) 2) r))) (* -1 (+ x (* -1 x)))) r))) (pow r 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) r)) (/ (* (+ x (* -1 x)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2)))) r)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2)))) r)) (* -1 (+ x (* -1 x)))) r))) (pow r 2))
(* -1 (* r (- (* -1 (/ x r)) 1)))
(+ r (* -1/2 (/ (pow x 2) r)))
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(+ r (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow r 5))) (* 1/8 (/ 1 (pow r 3))))) (* 1/2 (/ 1 r)))))
(+ r (* 1/2 (/ (* x (+ r (* -1 r))) r)))
(+ r (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2))))) r)) (* 1/2 (/ (+ r (* -1 r)) r)))))
(+ r (* x (+ (* 1/2 (/ (+ r (* -1 r)) r)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2)))) r)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2)))) (+ r (* -1 r)))) (pow r 3))))))))
(+ (sqrt r) (* -1/2 (* (sqrt (/ 1 r)) x)))
(+ (sqrt r) (* x (+ (* -1/2 (sqrt (/ 1 r))) (* -1/8 (* (sqrt (/ 1 (pow r 3))) x)))))
(+ (sqrt r) (* x (+ (* -1/2 (sqrt (/ 1 r))) (* x (+ (* -1/8 (sqrt (/ 1 (pow r 3)))) (* -1/16 (* (sqrt (/ 1 (pow r 5))) x)))))))
(+ r (* -1 x))
(+ (sqrt r) (* 1/2 (* (sqrt (/ 1 r)) x)))
(+ (sqrt r) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow r 3))) x)) (* 1/2 (sqrt (/ 1 r))))))
(+ (sqrt r) (* x (+ (* 1/2 (sqrt (/ 1 r))) (* x (+ (* -1/8 (sqrt (/ 1 (pow r 3)))) (* 1/16 (* (sqrt (/ 1 (pow r 5))) x)))))))
(+ (* x (+ r (* -1 r))) (pow r 2))
(+ (* x (+ r (+ (* -1 r) (* -1 x)))) (pow r 2))
(+ (/ 1 (pow r 2)) (/ (pow x 2) (pow r 4)))
(+ (* (pow x 2) (+ (/ 1 (pow r 4)) (/ (pow x 2) (pow r 6)))) (/ 1 (pow r 2)))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (/ 1 (pow r 6)) (/ (pow x 2) (pow r 8)))) (/ 1 (pow r 4)))) (/ 1 (pow r 2)))
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(* (pow x 2) (- (/ r (pow x 2)) (* 1/2 (/ 1 r))))
(* x (+ (sqrt -1) (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ r (* -1 r)) (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))))
(* x (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow r 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (/ r x) 1))
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* r (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow r 2) (sqrt (/ 1 (pow x 5))))) (* 1/2 (* r (sqrt (/ 1 (pow x 3))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow r 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (pow r 3) (sqrt (/ 1 (pow x 7))))) (* 1/2 (* r (sqrt (/ 1 (pow x 3)))))))))
(* (pow x 2) (- (+ (* -1 (/ r x)) (/ r x)) 1))
(* (pow x 2) (- (+ (* -1 (/ r x)) (+ (/ r x) (/ (pow r 2) (pow x 2)))) 1))
(/ (- (* -1 (/ (+ r (* -1 r)) x)) 1) (pow x 2))
(/ (- (* -1 (/ (+ (pow r 2) (pow (+ r (* -1 r)) 2)) (pow x 2))) (+ 1 (+ (* -1 (/ r x)) (/ r x)))) (pow x 2))
(/ (- (* -1 (/ (+ (* (+ r (* -1 r)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) (* (pow r 2) (+ r (* -1 r)))) (pow x 3))) (+ 1 (+ (* -1 (/ r x)) (+ (/ r x) (+ (/ (pow r 2) (pow x 2)) (/ (pow (+ r (* -1 r)) 2) (pow x 2))))))) (pow x 2))
(* x (+ 1 (/ r x)))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ r (* -1 r)) (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (* (pow r 3) (sqrt -1)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow r 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* (pow x 2) (- (* -1 (/ (+ r (* -1 r)) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ r (+ (* -1 r) (* -1 (/ (pow r 2) x)))) x)) 1))
(/ (- (+ (* -1 (/ r x)) (/ r x)) 1) (pow x 2))
(/ (- (* -1 (/ (- (+ (/ (pow r 2) x) (/ (pow (+ r (* -1 r)) 2) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ r (* -1 r)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x) (/ (* (pow r 2) (+ r (* -1 r))) x)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(* -1 (* x (- (* -1 (/ r x)) 1)))
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@inf
((sqrt (+ (* r r) (* (neg x) x))) (+ (* r r) (* (neg x) x)) (* (neg x) x) (neg x) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/2 r) x) x) r) (* (/ -1/2 r) x) (/ -1/2 r) (* (sqrt (- r x)) (sqrt (+ x r))) (sqrt (- r x)) (- r x) (sqrt (+ x r)) (/ 1 (pow (* (- r x) (+ x r)) -1)) (sqrt (/ 1 (pow (* (- r x) (+ x r)) -1))) (pow (* (- r x) (+ x r)) -1) (* (- r x) (+ x r)) (+ x r))
5.0ms
r
@inf
((sqrt (+ (* r r) (* (neg x) x))) (+ (* r r) (* (neg x) x)) (* (neg x) x) (neg x) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/2 r) x) x) r) (* (/ -1/2 r) x) (/ -1/2 r) (* (sqrt (- r x)) (sqrt (+ x r))) (sqrt (- r x)) (- r x) (sqrt (+ x r)) (/ 1 (pow (* (- r x) (+ x r)) -1)) (sqrt (/ 1 (pow (* (- r x) (+ x r)) -1))) (pow (* (- r x) (+ x r)) -1) (* (- r x) (+ x r)) (+ x r))
4.0ms
r
@0
((sqrt (+ (* r r) (* (neg x) x))) (+ (* r r) (* (neg x) x)) (* (neg x) x) (neg x) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/2 r) x) x) r) (* (/ -1/2 r) x) (/ -1/2 r) (* (sqrt (- r x)) (sqrt (+ x r))) (sqrt (- r x)) (- r x) (sqrt (+ x r)) (/ 1 (pow (* (- r x) (+ x r)) -1)) (sqrt (/ 1 (pow (* (- r x) (+ x r)) -1))) (pow (* (- r x) (+ x r)) -1) (* (- r x) (+ x r)) (+ x r))
4.0ms
r
@-inf
((sqrt (+ (* r r) (* (neg x) x))) (+ (* r r) (* (neg x) x)) (* (neg x) x) (neg x) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/2 r) x) x) r) (* (/ -1/2 r) x) (/ -1/2 r) (* (sqrt (- r x)) (sqrt (+ x r))) (sqrt (- r x)) (- r x) (sqrt (+ x r)) (/ 1 (pow (* (- r x) (+ x r)) -1)) (sqrt (/ 1 (pow (* (- r x) (+ x r)) -1))) (pow (* (- r x) (+ x r)) -1) (* (- r x) (+ x r)) (+ x r))
3.0ms
x
@0
((sqrt (+ (* r r) (* (neg x) x))) (+ (* r r) (* (neg x) x)) (* (neg x) x) (neg x) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/2 r) x) x) r) (* (/ -1/2 r) x) (/ -1/2 r) (* (sqrt (- r x)) (sqrt (+ x r))) (sqrt (- r x)) (- r x) (sqrt (+ x r)) (/ 1 (pow (* (- r x) (+ x r)) -1)) (sqrt (/ 1 (pow (* (- r x) (+ x r)) -1))) (pow (* (- r x) (+ x r)) -1) (* (- r x) (+ x r)) (+ x r))

simplify155.0ms (3.9%)

Memory
-30.3MiB live, 44.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06953043
122452438
094702290
Stop Event
1×iter limit
1×node limit
Counts
137 → 135
Calls
Call 1
Inputs
(* x (sqrt -1))
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (pow r 2))
(* -1 r)
(* -1/2 (/ (pow x 2) r))
(/ (+ (* -1/2 (pow x 2)) (pow r 2)) r)
(* -1/2 (/ x r))
(/ -1/2 r)
(+ (* 1/2 (/ (* r (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* r (+ (* 1/2 (/ (* r (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))) (* x (sqrt -1)))
(+ (* r (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* r (+ (* -1/4 (/ (* r (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))) (* x (sqrt -1)))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 x)))) (* (sqrt x) (sqrt -1)))
(+ (* r (+ (* -1/8 (* (/ r (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 3))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* r (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* r (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ r (pow (sqrt -1) 5)) (sqrt (/ 1 (pow x 5))))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(- r x)
(sqrt x)
(+ (sqrt x) (* 1/2 (* r (sqrt (/ 1 x)))))
(+ (sqrt x) (* r (+ (* -1/8 (* r (sqrt (/ 1 (pow x 3))))) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* r (+ (* 1/2 (sqrt (/ 1 x))) (* r (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* r (sqrt (/ 1 (pow x 5))))))))))
(+ (* -1 (pow x 2)) (* r (+ x (* -1 x))))
(+ (* -1 (pow x 2)) (* r (+ r (+ x (* -1 x)))))
(/ -1 (pow x 2))
(- (* -1 (/ (pow r 2) (pow x 4))) (/ 1 (pow x 2)))
(- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 6))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(- (* (pow r 2) (- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
x
(+ r x)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(pow r 2)
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(* r (+ 1 (* 1/2 (/ (+ x (* -1 x)) r))))
(* r (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2))))))
(* r (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow r 3))) (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2)))))))
(sqrt r)
(* r (+ (sqrt (/ 1 r)) (* -1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* -1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3)))))))
(* r (+ 1 (* -1 (/ x r))))
(* r (+ (sqrt (/ 1 r)) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)))))
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))))
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (/ x r))))
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (/ x r)))))
(/ 1 (pow r 2))
(/ (+ 1 (* -1 (/ (+ x (* -1 x)) r))) (pow r 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))) (pow r 2)))) (+ (* -1 (/ x r)) (/ x r))) (pow r 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ x (* -1 x)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))))) (* (pow x 2) (+ x (* -1 x)))) (pow r 3)))) (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow r 2))) (/ x r))))) (pow r 2))
(* r (+ 1 (/ x r)))
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4)))))))
(* -1 (* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(* -1 (* r (- (* 1/2 (/ (pow x 2) (pow r 2))) 1)))
(* -1 (* r (pow (sqrt -1) 2)))
(* -1 (* r (+ (* -1/2 (/ (+ x (* -1 x)) r)) (pow (sqrt -1) 2))))
(* -1 (* r (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) r)) (* 1/2 (+ x (* -1 x)))) r)) (pow (sqrt -1) 2))))
(* -1 (* r (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* r (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) r)) (* 1/2 (+ x (* -1 x)))) r)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt r) (pow (sqrt -1) 2)))
(* -1 (* r (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (* (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2))))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (* (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (* (pow x 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))))
(* -1 (* r (- (/ x r) 1)))
(* -1 (* r (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (/ (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2))))))
(* -1 (* r (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (/ (pow x 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (/ (pow x 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* (sqrt (/ 1 r)) (pow (sqrt -1) 2)))))))
(* (pow r 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) r)) r))))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow x 2) r)) (* -1 (/ (pow (+ x (* -1 x)) 2) r))) (* -1 (+ x (* -1 x)))) r))) (pow r 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) r)) (/ (* (+ x (* -1 x)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2)))) r)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2)))) r)) (* -1 (+ x (* -1 x)))) r))) (pow r 2))
(* -1 (* r (- (* -1 (/ x r)) 1)))
(+ r (* -1/2 (/ (pow x 2) r)))
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(+ r (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow r 5))) (* 1/8 (/ 1 (pow r 3))))) (* 1/2 (/ 1 r)))))
(+ r (* 1/2 (/ (* x (+ r (* -1 r))) r)))
(+ r (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2))))) r)) (* 1/2 (/ (+ r (* -1 r)) r)))))
(+ r (* x (+ (* 1/2 (/ (+ r (* -1 r)) r)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2)))) r)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow r 2)))) (+ r (* -1 r)))) (pow r 3))))))))
(+ (sqrt r) (* -1/2 (* (sqrt (/ 1 r)) x)))
(+ (sqrt r) (* x (+ (* -1/2 (sqrt (/ 1 r))) (* -1/8 (* (sqrt (/ 1 (pow r 3))) x)))))
(+ (sqrt r) (* x (+ (* -1/2 (sqrt (/ 1 r))) (* x (+ (* -1/8 (sqrt (/ 1 (pow r 3)))) (* -1/16 (* (sqrt (/ 1 (pow r 5))) x)))))))
(+ r (* -1 x))
(+ (sqrt r) (* 1/2 (* (sqrt (/ 1 r)) x)))
(+ (sqrt r) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow r 3))) x)) (* 1/2 (sqrt (/ 1 r))))))
(+ (sqrt r) (* x (+ (* 1/2 (sqrt (/ 1 r))) (* x (+ (* -1/8 (sqrt (/ 1 (pow r 3)))) (* 1/16 (* (sqrt (/ 1 (pow r 5))) x)))))))
(+ (* x (+ r (* -1 r))) (pow r 2))
(+ (* x (+ r (+ (* -1 r) (* -1 x)))) (pow r 2))
(+ (/ 1 (pow r 2)) (/ (pow x 2) (pow r 4)))
(+ (* (pow x 2) (+ (/ 1 (pow r 4)) (/ (pow x 2) (pow r 6)))) (/ 1 (pow r 2)))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (/ 1 (pow r 6)) (/ (pow x 2) (pow r 8)))) (/ 1 (pow r 4)))) (/ 1 (pow r 2)))
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(* (pow x 2) (- (/ r (pow x 2)) (* 1/2 (/ 1 r))))
(* x (+ (sqrt -1) (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ r (* -1 r)) (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))))
(* x (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow r 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (/ r x) 1))
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* r (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow r 2) (sqrt (/ 1 (pow x 5))))) (* 1/2 (* r (sqrt (/ 1 (pow x 3))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow r 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (pow r 3) (sqrt (/ 1 (pow x 7))))) (* 1/2 (* r (sqrt (/ 1 (pow x 3)))))))))
(* (pow x 2) (- (+ (* -1 (/ r x)) (/ r x)) 1))
(* (pow x 2) (- (+ (* -1 (/ r x)) (+ (/ r x) (/ (pow r 2) (pow x 2)))) 1))
(/ (- (* -1 (/ (+ r (* -1 r)) x)) 1) (pow x 2))
(/ (- (* -1 (/ (+ (pow r 2) (pow (+ r (* -1 r)) 2)) (pow x 2))) (+ 1 (+ (* -1 (/ r x)) (/ r x)))) (pow x 2))
(/ (- (* -1 (/ (+ (* (+ r (* -1 r)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) (* (pow r 2) (+ r (* -1 r)))) (pow x 3))) (+ 1 (+ (* -1 (/ r x)) (+ (/ r x) (+ (/ (pow r 2) (pow x 2)) (/ (pow (+ r (* -1 r)) 2) (pow x 2))))))) (pow x 2))
(* x (+ 1 (/ r x)))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ r (* -1 r)) (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (* (pow r 3) (sqrt -1)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow r 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* (pow x 2) (- (* -1 (/ (+ r (* -1 r)) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ r (+ (* -1 r) (* -1 (/ (pow r 2) x)))) x)) 1))
(/ (- (+ (* -1 (/ r x)) (/ r x)) 1) (pow x 2))
(/ (- (* -1 (/ (- (+ (/ (pow r 2) x) (/ (pow (+ r (* -1 r)) 2) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ r (* -1 r)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x) (/ (* (pow r 2) (+ r (* -1 r))) x)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(* -1 (* x (- (* -1 (/ r x)) 1)))
Outputs
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (*.f64 (/.f64 r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)) r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* -1/8 (/ (pow r 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 r r) (*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (*.f64 r r) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow r 2) (+ (* (pow r 2) (- (* 1/16 (/ (pow r 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 r (/.f64 r (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 r r) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (*.f64 r r) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (pow r 2))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(* -1 r)
(neg.f64 r)
(* -1/2 (/ (pow x 2) r))
(*.f64 (/.f64 (*.f64 x x) r) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (pow x 2)) (pow r 2)) r)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) (*.f64 r r)) r)
(* -1/2 (/ x r))
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
(/ -1/2 r)
(/.f64 #s(literal -1/2 binary64) r)
(+ (* 1/2 (/ (* r (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ (* r (+ (* 1/2 (/ (* r (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))) (* x (sqrt -1)))
(fma.f64 (*.f64 r #s(literal 1/2 binary64)) (/.f64 r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(+ (* r (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* r (+ (* -1/4 (/ (* r (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 r (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) r (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (/ r (sqrt -1)) (sqrt (/ 1 x)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (*.f64 r #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* r (+ (* -1/8 (* (/ r (pow (sqrt -1) 3)) (sqrt (/ 1 (pow x 3))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 r #s(literal -1/8 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) r (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* r (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* r (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ r (pow (sqrt -1) 5)) (sqrt (/ 1 (pow x 5))))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 r (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) r (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) r (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(* -1 x)
(neg.f64 x)
(- r x)
(-.f64 r x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* r (sqrt (/ 1 x)))))
(fma.f64 (*.f64 r #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* r (+ (* -1/8 (* r (sqrt (/ 1 (pow x 3))))) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (*.f64 r #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) r (sqrt.f64 x))
(+ (sqrt x) (* r (+ (* 1/2 (sqrt (/ 1 x))) (* r (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* r (sqrt (/ 1 (pow x 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) r) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) r (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) r (sqrt.f64 x))
(+ (* -1 (pow x 2)) (* r (+ x (* -1 x))))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (* r (+ r (+ x (* -1 x)))))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(- (* -1 (/ (pow r 2) (pow x 4))) (/ 1 (pow x 2)))
(neg.f64 (fma.f64 r (/.f64 r (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x)))
(- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 6))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(fma.f64 (neg.f64 (fma.f64 r (/.f64 r (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 r r) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(- (* (pow r 2) (- (* (pow r 2) (- (* -1 (/ (pow r 2) (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(fma.f64 (fma.f64 (neg.f64 (fma.f64 r (/.f64 r (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 r r) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 r r) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
x
(+ r x)
(+.f64 x r)
r
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) r) r) #s(literal -1/2 binary64) #s(literal 1 binary64)) r)
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) r) r) #s(literal -1/2 binary64) #s(literal 1 binary64))) r)
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (+ (* -1/8 (/ (pow x 4) (pow r 4))) (* -1/16 (/ (pow x 6) (pow r 6)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 r #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) r) (/.f64 (*.f64 x x) r) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 r #s(literal 4 binary64))))) r r)
(pow r 2)
(*.f64 r r)
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) r) r)) r) r)
(* r (+ 1 (* 1/2 (/ (+ x (* -1 x)) r))))
r
(* r (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 x) x) (*.f64 r r)) #s(literal 1/2 binary64) #s(literal 1 binary64)) r)
(* r (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow r 3))) (+ (* 1/2 (/ (+ x (* -1 x)) r)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow r 2)))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 x) x) (*.f64 r r)) #s(literal 1/2 binary64) #s(literal 1 binary64)) r)
(sqrt r)
(sqrt.f64 r)
(* r (+ (sqrt (/ 1 r)) (* -1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r))) r)
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r)))) r)
(* r (+ (sqrt (/ 1 r)) (+ (* -1/2 (* (sqrt (/ 1 (pow r 3))) x)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* -1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3)))))))
(*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r))) r)
(* r (+ 1 (* -1 (/ x r))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x r)) r)
(* r (+ (sqrt (/ 1 r)) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r))) r)
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r)))) r)
(* r (+ (sqrt (/ 1 r)) (+ (* -1/8 (* (sqrt (/ 1 (pow r 5))) (pow x 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow r 7))) (pow x 3))) (* 1/2 (* (sqrt (/ 1 (pow r 3))) x))))))
(*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 7 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 5 binary64)))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 r #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) r)))) r)
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (/ x r))))
(*.f64 r r)
(* (pow r 2) (+ 1 (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (/ x r)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) r) r)) r) r)
(/ 1 (pow r 2))
(/.f64 (/.f64 #s(literal 1 binary64) r) r)
(/ (+ 1 (* -1 (/ (+ x (* -1 x)) r))) (pow r 2))
(/.f64 (/.f64 #s(literal 1 binary64) r) r)
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))) (pow r 2)))) (+ (* -1 (/ x r)) (/ x r))) (pow r 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 x) x) (*.f64 r r))) (*.f64 r r))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ x (* -1 x)) (+ (* -1 (pow x 2)) (* -1 (pow (+ x (* -1 x)) 2))))) (* (pow x 2) (+ x (* -1 x)))) (pow r 3)))) (+ (* -1 (/ x r)) (+ (* -1 (/ (pow x 2) (pow r 2))) (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow r 2))) (/ x r))))) (pow r 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 x) x) (*.f64 r r))) (*.f64 r r))
(* r (+ 1 (/ x r)))
(fma.f64 (/.f64 x r) r r)
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
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(*.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 r #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow r 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow r 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 r #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (+.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (*.f64 (pow.f64 r #s(literal 6 binary64)) #s(literal 1/16 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 r (/.f64 r x)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ r (* -1 r)) (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow r 2) (* 1/4 (/ (pow (+ r (* -1 r)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ r (* -1 r)) (sqrt -1)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) r)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) r) r)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) r)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (* (pow r 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (* (pow r 3) (sqrt -1)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* (* r (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 r #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) r) r)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) r)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 r x)) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(* -1 (* x (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) r) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 r (/.f64 r #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) r) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (/ (pow r 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow r 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* r (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 r #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 r (/.f64 r #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) r) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))) (neg.f64 x))
(* (pow x 2) (- (* -1 (/ (+ r (* -1 r)) x)) 1))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* -1 (/ (+ r (+ (* -1 r) (* -1 (/ (pow r 2) x)))) x)) 1))
(*.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 r) r) x) (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (*.f64 x x))
(/ (- (+ (* -1 (/ r x)) (/ r x)) 1) (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ (- (* -1 (/ (- (+ (/ (pow r 2) x) (/ (pow (+ r (* -1 r)) 2) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(/.f64 (neg.f64 (fma.f64 (/.f64 r x) (/.f64 r x) #s(literal 1 binary64))) (*.f64 x x))
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ r (* -1 r)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x) (/ (* (pow r 2) (+ r (* -1 r))) x)) (+ (pow r 2) (pow (+ r (* -1 r)) 2))) x)) (+ r (* -1 r))) x)) 1) (pow x 2))
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 (neg.f64 r) r) (neg.f64 x)) x) #s(literal -1 binary64) #s(literal -1 binary64)) (*.f64 x x))
(* -1 (* x (- (* -1 (/ r x)) 1)))
(fma.f64 (/.f64 (neg.f64 r) x) (neg.f64 x) x)

rewrite256.0ms (6.4%)

Memory
-11.7MiB live, 76.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029129
048120
1173120
21122120
0940587
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
19 → 1 684
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(fma.f64 r r (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r)
(*.f64 (/.f64 #s(literal -1/2 binary64) r) x)
(/.f64 #s(literal -1/2 binary64) r)
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(sqrt.f64 (-.f64 r x))
(-.f64 r x)
(sqrt.f64 (+.f64 x r))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
(pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))
(*.f64 (-.f64 r x) (+.f64 x r))
(+.f64 x r)
Outputs
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x r))) (sqrt.f64 (-.f64 r x)))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 r x))) (sqrt.f64 (+.f64 x r)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 x r)) (pow.f64 (-.f64 r x) #s(literal 1/4 binary64))) (pow.f64 (-.f64 r x) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (-.f64 r x)) (pow.f64 (+.f64 x r) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x r) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (hypot.f64 x r)) (sqrt.f64 (hypot.f64 x r)))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 r x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (+.f64 x r) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (hypot.f64 x r))
(*.f64 (pow.f64 (hypot.f64 x r) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 x r) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x r) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 r x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x r) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (-.f64 r x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 r x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 x r) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 x r))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (pow.f64 (pow.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 x r) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (hypot.f64 x r) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 x r))))
(*.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 x r))
(*.f64 (sqrt.f64 (+.f64 x r)) (sqrt.f64 (-.f64 r x)))
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 x r))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))) (-.f64 r x))) (sqrt.f64 (-.f64 x r)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (-.f64 r x))) (sqrt.f64 (fma.f64 (-.f64 r x) r (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 x r))) (sqrt.f64 (fma.f64 x (+.f64 x r) (*.f64 r r))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (+.f64 x r))) (sqrt.f64 (+.f64 x r)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x r) (-.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 x (+.f64 x r) (*.f64 r r))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (-.f64 x r))) (sqrt.f64 (-.f64 x r)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 r x) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (-.f64 r x) r (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (*.f64 (-.f64 r x) (-.f64 x r)))) (sqrt.f64 (*.f64 (-.f64 r x) (-.f64 x r))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x r) (+.f64 x r))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64)))) (sqrt.f64 (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (*.f64 (-.f64 r x) x) #s(literal 3/2 binary64)) (pow.f64 (*.f64 (-.f64 r x) r) #s(literal 3/2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (*.f64 (-.f64 r x) x) #s(literal 2 binary64)) (*.f64 (*.f64 (-.f64 r x) r) (-.f64 (*.f64 (-.f64 r x) r) (*.f64 (-.f64 r x) x))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 r #s(literal 6 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))) (-.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (-.f64 x r) (fma.f64 x (+.f64 x r) (*.f64 r r)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)))) (hypot.f64 (pow.f64 r #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 r #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))))) (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 (*.f64 x (+.f64 x r)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (+.f64 x r) (fma.f64 (-.f64 r x) r (*.f64 x x)))))
(/.f64 (sqrt.f64 (hypot.f64 x r)) (sqrt.f64 (pow.f64 (hypot.f64 x r) #s(literal -1 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 x r)))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (sqrt.f64 (*.f64 (fma.f64 (-.f64 r x) r (*.f64 x x)) (fma.f64 x (+.f64 x r) (*.f64 r r)))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64))) (pow.f64 (*.f64 x r) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 r #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))) (neg.f64 (hypot.f64 x r)))
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(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x r) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (+.f64 x r)))
(fma.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x) r)
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) r)
(fma.f64 (pow.f64 (sqrt.f64 r) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 r) #s(literal 1 binary64)) x)
(fma.f64 (sqrt.f64 r) (sqrt.f64 r) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) r)
(fma.f64 #s(literal -1 binary64) (neg.f64 r) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) r)
(fma.f64 #s(literal 1 binary64) x r)
(fma.f64 #s(literal 1 binary64) r x)
(fma.f64 (neg.f64 r) #s(literal -1 binary64) x)
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x r) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 r r) (-.f64 x r))))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) r)
(fma.f64 x #s(literal 1 binary64) r)
(fma.f64 r #s(literal 1 binary64) x)
(-.f64 (-.f64 r #s(literal 0 binary64)) (neg.f64 x))
(-.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))) (-.f64 r x)) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64))) (-.f64 r x)))
(-.f64 (/.f64 (/.f64 (pow.f64 r #s(literal 6 binary64)) (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 r x)) (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 r r) (pow.f64 (hypot.f64 x r) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 r x)))
(-.f64 (/.f64 (*.f64 r r) (-.f64 r x)) (/.f64 (*.f64 x x) (-.f64 r x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x r)) (/.f64 (*.f64 r r) (-.f64 x r)))
(-.f64 r (neg.f64 x))
(+.f64 (-.f64 r #s(literal 0 binary64)) x)
(+.f64 (/.f64 (*.f64 x x) (-.f64 x r)) (neg.f64 (/.f64 (*.f64 r r) (-.f64 x r))))
(+.f64 x r)
(+.f64 r x)
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x r)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x r)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x r) #s(literal -1 binary64))) #s(literal -1 binary64)))

eval152.0ms (3.8%)

Memory
42.4MiB live, 117.2MiB allocated
Compiler

Compiled 28 808 to 4 364 computations (84.9% saved)

prune22.0ms (0.6%)

Memory
-31.7MiB live, 46.3MiB allocated
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1 20141 205
Fresh224
Picked235
Done000
Total1 20591 214
Accuracy
100.0%
Counts
1 214 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
99.7%
(sqrt.f64 (fma.f64 (-.f64 r x) x (*.f64 (-.f64 r x) r)))
99.7%
(sqrt.f64 (fma.f64 (+.f64 x r) (neg.f64 x) (*.f64 (+.f64 x r) r)))
99.7%
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
99.7%
(sqrt.f64 (fma.f64 x r (fma.f64 (neg.f64 x) x (*.f64 (-.f64 r x) r))))
✓99.8%
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
99.8%
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
60.0%
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
✓79.3%
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
Compiler

Compiled 260 to 129 computations (50.4% saved)

regimes20.0ms (0.5%)

Memory
15.2MiB live, 15.2MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(sqrt.f64 (fma.f64 (-.f64 r x) x (*.f64 (-.f64 r x) r)))
(sqrt.f64 (fma.f64 (+.f64 x r) (neg.f64 x) (*.f64 (+.f64 x r) r)))
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(sqrt.f64 (fma.f64 x r (fma.f64 (neg.f64 x) x (*.f64 (-.f64 r x) r))))
(sqrt.f64 #s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (-.f64 r x) (+.f64 x r)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Outputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
Calls

6 calls:

3.0ms
x
3.0ms
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
3.0ms
(pow.f64 x #s(literal 2 binary64))
3.0ms
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms
(pow.f64 r #s(literal 2 binary64))
Results
AccuracySegmentsBranch
99.8%1r
99.8%1x
99.8%1(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
99.8%1(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
99.8%1(pow.f64 r #s(literal 2 binary64))
99.8%1(pow.f64 x #s(literal 2 binary64))
Compiler

Compiled 23 to 25 computations (-8.7% saved)

regimes10.0ms (0.3%)

Memory
10.6MiB live, 10.6MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
Outputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
Calls

6 calls:

2.0ms
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
2.0ms
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms
(pow.f64 x #s(literal 2 binary64))
2.0ms
x
2.0ms
(pow.f64 r #s(literal 2 binary64))
Results
AccuracySegmentsBranch
99.8%1r
99.8%1x
99.8%1(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
99.8%1(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
99.8%1(pow.f64 r #s(literal 2 binary64))
99.8%1(pow.f64 x #s(literal 2 binary64))
Compiler

Compiled 23 to 25 computations (-8.7% saved)

regimes8.0ms (0.2%)

Memory
9.6MiB live, 9.6MiB allocated
Accuracy

Total -37.4b remaining (-146.3%)

Threshold costs -37.4b (-146.3%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
Outputs
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
Calls

6 calls:

1.0ms
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms
(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms
(pow.f64 r #s(literal 2 binary64))
1.0ms
(pow.f64 x #s(literal 2 binary64))
1.0ms
x
Results
AccuracySegmentsBranch
60.0%1r
60.0%1x
60.0%1(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
60.0%1(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
60.0%1(pow.f64 r #s(literal 2 binary64))
60.0%1(pow.f64 x #s(literal 2 binary64))
Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify62.0ms (1.6%)

Memory
13.0MiB live, 13.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
12727
23527
34427
45727
58127
613927
739927
8345527
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)
Outputs
(sqrt.f64 (fma.f64 r r (*.f64 (neg.f64 x) x)))
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (* (sqrt (- r x)) (sqrt (+ x r))) r)

soundness362.0ms (9.1%)

Memory
7.3MiB live, 7.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721
01121
14221
224321
3215821
0924921
06953043
122452438
094702290
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 77 to 52 computations (32.5% saved)

preprocess71.0ms (1.8%)

Memory
-59.1MiB live, 19.7MiB allocated
Remove

(abs r)

(abs x)

Compiler

Compiled 102 to 70 computations (31.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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