sqrt(r^2-x^2)

Time bar (total: 3.8s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze19.0ms (0.5%)

Memory
7.7MiB live, 7.7MiB 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)

sample1.3s (34.3%)

Memory
81.2MiB live, 704.1MiB allocated
Samples
902.0ms8 256×0valid
21.0ms264×0invalid
Precisions
Click to see histograms. Total time spent on operations: 624.0ms
ival-<=: 259.0ms (41.5% of total)
ival-pow2: 208.0ms (33.3% of total)
ival-sqrt: 66.0ms (10.6% of total)
ival-sub: 45.0ms (7.2% of total)
ival-and: 28.0ms (4.5% of total)
exact: 14.0ms (2.2% of total)
ival-assert: 3.0ms (0.5% of total)
Bogosity

explain100.0ms (2.6%)

Memory
-35.2MiB live, 39.7MiB 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: 18.0ms
ival-pow2: 11.0ms (61.4% of total)
ival-sqrt: 4.0ms (22.3% of total)
ival-sub: 2.0ms (11.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess409.0ms (10.8%)

Memory
45.2MiB live, 45.2MiB 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
▶99.8%
(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)

simplify353.0ms (9.3%)

Memory
-39.3MiB live, 40.1MiB 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

localize22.0ms (0.6%)

Memory
8.8MiB live, 8.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(pow.f64 r #s(literal 2 binary64))
accuracy0.00390625
(pow.f64 x #s(literal 2 binary64))
accuracy0.12890625
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
accuracy0.2109375
(-.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: 9.0ms
ival-pow2: 5.0ms (57% of total)
ival-sqrt: 2.0ms (22.8% of total)
ival-sub: 1.0ms (11.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory
2.6MiB 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
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
x
@inf
((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))
1.0ms
r
@-inf
((sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (pow r 2) (pow x 2))

simplify264.0ms (7%)

Memory
-57.8MiB live, 47.5MiB 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)))

rewrite168.0ms (4.4%)

Memory
55.6MiB 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)))

eval63.0ms (1.7%)

Memory
-53.4MiB live, 30.2MiB allocated
Compiler

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

prune8.0ms (0.2%)

Memory
14.0MiB live, 14.0MiB allocated
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3028310
Fresh000
Picked101
Done000
Total3038311
Accuracy
100.0%
Counts
311 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
99.7%
(sqrt.f64 (fma.f64 (pow.f64 r #s(literal 3/2 binary64)) (sqrt.f64 r) (*.f64 (neg.f64 x) x)))
▶99.8%
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
▶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))))
▶89.4%
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
82.6%
#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 222 to 162 computations (27% saved)

simplify169.0ms (4.4%)

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

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
cost-diff0
(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))
cost-diff0
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
cost-diff2
(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)
cost-diff0
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
cost-diff0
#s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x)))
cost-diff0
(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))))
cost-diff5
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
cost-diff0
(*.f64 r r)
cost-diff0
(neg.f64 x)
cost-diff0
(fma.f64 (neg.f64 x) x (*.f64 r r))
cost-diff0
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
cost-diff0
(neg.f64 r)
cost-diff0
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
cost-diff0
(+.f64 x r)
cost-diff0
(-.f64 r x)
cost-diff0
(*.f64 (-.f64 r x) (+.f64 x r))
cost-diff0
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035215
060210
1100210
2177210
3414210
41064204
52088200
64633200
77582200
08018196
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
(*.f64 (-.f64 r x) (+.f64 x r))
(-.f64 r x)
r
x
(+.f64 x r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
r
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(neg.f64 x)
x
(*.f64 r r)
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))))
#s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x)))
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
(/.f64 (/.f64 r x) x)
(/.f64 r x)
r
x
#s(literal -1 binary64)
(*.f64 x x)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
(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)
(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 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
#s(literal -1/8 binary64)
(pow.f64 r #s(literal 3 binary64))
r
#s(literal 3 binary64)
x
(/.f64 #s(literal -1/2 binary64) r)
#s(literal -1/2 binary64)
(*.f64 x x)
Outputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(*.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(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
r
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(neg.f64 x)
x
(*.f64 r r)
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 #s(approx (- (pow r 2) (pow x 2)) (fma.f64 (neg.f64 x) x (*.f64 r r))))
#s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x)))
#s(approx (- (pow r 2) (pow x 2)) (fma.f64 (neg.f64 x) x (*.f64 r r)))
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
(/.f64 (/.f64 r x) x)
(/.f64 r x)
r
x
#s(literal -1 binary64)
(*.f64 x x)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (fma.f64 (pow.f64 (/.f64 x r) #s(literal 3 binary64)) #s(literal -1/8 binary64) (*.f64 (/.f64 x r) #s(literal -1/2 binary64))) x 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)
(fma.f64 (fma.f64 (pow.f64 (/.f64 x r) #s(literal 3 binary64)) #s(literal -1/8 binary64) (*.f64 (/.f64 x r) #s(literal -1/2 binary64))) x r)
(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 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
#s(literal -1/8 binary64)
(pow.f64 r #s(literal 3 binary64))
r
#s(literal 3 binary64)
x
(/.f64 #s(literal -1/2 binary64) r)
#s(literal -1/2 binary64)
(*.f64 x x)

localize111.0ms (2.9%)

Memory
-44.1MiB live, 35.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.20703125
(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))
accuracy0.2421875
(*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
accuracy0.28125
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
accuracy6.798232435919211
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
accuracy0.12890625
(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))))
accuracy0.2578125
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
accuracy0.265625
(/.f64 (/.f64 r x) x)
accuracy0.38671875
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
accuracy0.0
(*.f64 r r)
accuracy0.0
(neg.f64 x)
accuracy0.12890625
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
accuracy0.21875
(fma.f64 (neg.f64 x) x (*.f64 r r))
accuracy0.0
(neg.f64 r)
accuracy62.984546073614155
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
accuracy0.0
(-.f64 r x)
accuracy0.0
(+.f64 x r)
accuracy0.0390625
(*.f64 (-.f64 r x) (+.f64 x r))
accuracy0.12890625
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
Samples
90.0ms256×0valid
Compiler

Compiled 177 to 36 computations (79.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-div: 34.0ms (46.3% of total)
ival-mult: 15.0ms (20.4% of total)
ival-add: 6.0ms (8.2% of total)
ival-sqrt: 5.0ms (6.8% of total)
ival-pow2: 5.0ms (6.8% of total)
ival-sub: 3.0ms (4.1% of total)
ival-pow: 3.0ms (4.1% of total)
ival-neg: 2.0ms (2.7% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series30.0ms (0.8%)

Memory
13.9MiB live, 13.9MiB allocated
Counts
20 → 93
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
(*.f64 (-.f64 r x) (+.f64 x r))
(-.f64 r x)
(+.f64 x r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(neg.f64 x)
(*.f64 r r)
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
(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))))
#s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x)))
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
(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)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
(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 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
(/.f64 (/.f64 r x) x)
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
Outputs
(* x (sqrt -1))
(+ (* 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)))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (* r (+ x (* -1 x))))
(+ (* -1 (pow x 2)) (* r (+ r (+ x (* -1 x)))))
(* -1 x)
(- r x)
x
(+ r x)
(+ (* 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 r)
(+ (* -1 (pow x 2)) (pow r 2))
(pow r 2)
(- (pow r 2) (pow x 2))
-1
(- (/ (pow r 2) (pow x 2)) 1)
(* -1/8 (/ (pow x 4) (pow r 3)))
(/ (+ (* -1/2 (* (pow r 2) (pow x 2))) (* -1/8 (pow x 4))) (pow r 3))
(/ (+ (* -1/8 (pow x 4)) (* (pow r 2) (+ (* -1/2 (pow x 2)) (pow r 2)))) (pow r 3))
(* -1/8 (/ (pow x 2) (pow r 3)))
(/ (+ (* -1/2 (pow r 2)) (* -1/8 (pow x 2))) (pow r 3))
(* -1/8 (/ x (pow r 3)))
(/ r (pow x 2))
(/ -1/8 (pow r 3))
r
(* 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)))))))
(* (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)))))
(* r (+ 1 (* -1 (/ x r))))
(* r (+ 1 (/ 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) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(/ (pow r 2) (pow x 2))
(* (pow r 2) (- (/ 1 (pow x 2)) (/ 1 (pow r 2))))
(/ -1/2 r)
(/ (- (* -1/8 (/ (pow x 2) (pow r 2))) 1/2) r)
(* -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))))
(* (pow r 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) r)) r))))
(* -1 (* r (- (/ x r) 1)))
(* -1 (* r (- (* -1 (/ x r)) 1)))
(* -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 (- (+ (* 1/8 (/ (pow x 4) (pow r 4))) (* 1/2 (/ (pow x 2) (pow r 2)))) 1)))
(* -1 (/ (+ 1/2 (* 1/8 (/ (pow x 2) (pow r 2)))) 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))))))))
(+ (* x (+ r (* -1 r))) (pow r 2))
(+ (* x (+ r (+ (* -1 r) (* -1 x)))) (pow r 2))
(+ r (* -1 x))
(+ 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))
(- (* -1/8 (/ (pow x 2) (pow r 3))) (* 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))))))))
(* (pow x 2) (- (+ (* -1 (/ r x)) (/ r x)) 1))
(* (pow x 2) (- (+ (* -1 (/ r x)) (+ (/ r x) (/ (pow r 2) (pow x 2)))) 1))
(* x (- (/ r x) 1))
(* x (+ 1 (/ r x)))
(* 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 (* (pow x 4) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(* (pow x 4) (- (/ r (pow x 4)) (+ (* 1/8 (/ 1 (pow r 3))) (/ 1/2 (* r (pow x 2))))))
(* -1 (* (pow x 2) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(* -1 (* x (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)))))
(* (pow x 2) (- (* -1 (/ (+ r (* -1 r)) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ r (+ (* -1 r) (* -1 (/ (pow r 2) x)))) x)) 1))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(* -1 (* x (- (* -1 (/ r x)) 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
6.0ms
x
@inf
((sqrt (* (- r x) (+ x r))) (* (- r x) (+ x r)) (- r x) (+ x r) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (+ (* (neg x) x) (* r r))) (+ (* (neg x) x) (* r r)) (neg x) (* r r) (* (+ (* (/ (/ r x) x) r) -1) (* x x)) (sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (+ (* (/ (/ r x) x) r) -1) (+ (* (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* x x)) r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* (/ -1/8 (pow r 3)) x) (/ (/ r x) x) (/ -1/8 (pow r 3)))
5.0ms
r
@-inf
((sqrt (* (- r x) (+ x r))) (* (- r x) (+ x r)) (- r x) (+ x r) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (+ (* (neg x) x) (* r r))) (+ (* (neg x) x) (* r r)) (neg x) (* r r) (* (+ (* (/ (/ r x) x) r) -1) (* x x)) (sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (+ (* (/ (/ r x) x) r) -1) (+ (* (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* x x)) r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* (/ -1/8 (pow r 3)) x) (/ (/ r x) x) (/ -1/8 (pow r 3)))
5.0ms
r
@0
((sqrt (* (- r x) (+ x r))) (* (- r x) (+ x r)) (- r x) (+ x r) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (+ (* (neg x) x) (* r r))) (+ (* (neg x) x) (* r r)) (neg x) (* r r) (* (+ (* (/ (/ r x) x) r) -1) (* x x)) (sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (+ (* (/ (/ r x) x) r) -1) (+ (* (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* x x)) r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* (/ -1/8 (pow r 3)) x) (/ (/ r x) x) (/ -1/8 (pow r 3)))
5.0ms
r
@inf
((sqrt (* (- r x) (+ x r))) (* (- r x) (+ x r)) (- r x) (+ x r) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (+ (* (neg x) x) (* r r))) (+ (* (neg x) x) (* r r)) (neg x) (* r r) (* (+ (* (/ (/ r x) x) r) -1) (* x x)) (sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (+ (* (/ (/ r x) x) r) -1) (+ (* (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* x x)) r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* (/ -1/8 (pow r 3)) x) (/ (/ r x) x) (/ -1/8 (pow r 3)))
4.0ms
x
@0
((sqrt (* (- r x) (+ x r))) (* (- r x) (+ x r)) (- r x) (+ x r) (sqrt (- (pow r 2) (pow x 2))) (neg r) (sqrt (+ (* (neg x) x) (* r r))) (+ (* (neg x) x) (* r r)) (neg x) (* r r) (* (+ (* (/ (/ r x) x) r) -1) (* x x)) (sqrt (- (pow r 2) (pow x 2))) (- (pow r 2) (pow x 2)) (+ (* (/ (/ r x) x) r) -1) (+ (* (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* x x)) r) (sqrt (- (pow r 2) (pow x 2))) (+ (* (* (/ -1/8 (pow r 3)) x) x) (/ -1/2 r)) (* (/ -1/8 (pow r 3)) x) (/ (/ r x) x) (/ -1/8 (pow r 3)))

simplify86.0ms (2.3%)

Memory
22.0MiB live, 22.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03971586
112561206
255061146
083641081
Stop Event
1×iter limit
1×node limit
Counts
93 → 91
Calls
Call 1
Inputs
(* x (sqrt -1))
(+ (* 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)))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (* r (+ x (* -1 x))))
(+ (* -1 (pow x 2)) (* r (+ r (+ x (* -1 x)))))
(* -1 x)
(- r x)
x
(+ r x)
(+ (* 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 r)
(+ (* -1 (pow x 2)) (pow r 2))
(pow r 2)
(- (pow r 2) (pow x 2))
-1
(- (/ (pow r 2) (pow x 2)) 1)
(* -1/8 (/ (pow x 4) (pow r 3)))
(/ (+ (* -1/2 (* (pow r 2) (pow x 2))) (* -1/8 (pow x 4))) (pow r 3))
(/ (+ (* -1/8 (pow x 4)) (* (pow r 2) (+ (* -1/2 (pow x 2)) (pow r 2)))) (pow r 3))
(* -1/8 (/ (pow x 2) (pow r 3)))
(/ (+ (* -1/2 (pow r 2)) (* -1/8 (pow x 2))) (pow r 3))
(* -1/8 (/ x (pow r 3)))
(/ r (pow x 2))
(/ -1/8 (pow r 3))
r
(* 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)))))))
(* (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)))))
(* r (+ 1 (* -1 (/ x r))))
(* r (+ 1 (/ 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) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(/ (pow r 2) (pow x 2))
(* (pow r 2) (- (/ 1 (pow x 2)) (/ 1 (pow r 2))))
(/ -1/2 r)
(/ (- (* -1/8 (/ (pow x 2) (pow r 2))) 1/2) r)
(* -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))))
(* (pow r 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) r)) r))))
(* -1 (* r (- (/ x r) 1)))
(* -1 (* r (- (* -1 (/ x r)) 1)))
(* -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 (- (+ (* 1/8 (/ (pow x 4) (pow r 4))) (* 1/2 (/ (pow x 2) (pow r 2)))) 1)))
(* -1 (/ (+ 1/2 (* 1/8 (/ (pow x 2) (pow r 2)))) 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))))))))
(+ (* x (+ r (* -1 r))) (pow r 2))
(+ (* x (+ r (+ (* -1 r) (* -1 x)))) (pow r 2))
(+ r (* -1 x))
(+ 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))
(- (* -1/8 (/ (pow x 2) (pow r 3))) (* 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))))))))
(* (pow x 2) (- (+ (* -1 (/ r x)) (/ r x)) 1))
(* (pow x 2) (- (+ (* -1 (/ r x)) (+ (/ r x) (/ (pow r 2) (pow x 2)))) 1))
(* x (- (/ r x) 1))
(* x (+ 1 (/ r x)))
(* 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 (* (pow x 4) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(* (pow x 4) (- (/ r (pow x 4)) (+ (* 1/8 (/ 1 (pow r 3))) (/ 1/2 (* r (pow x 2))))))
(* -1 (* (pow x 2) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(* -1 (* x (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)))))
(* (pow x 2) (- (* -1 (/ (+ r (* -1 r)) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ r (+ (* -1 r) (* -1 (/ (pow r 2) x)))) x)) 1))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(* -1 (* x (- (* -1 (/ r x)) 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 (/ (* r (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 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 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) r) r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* 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 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) r) r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) 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 x)
(neg.f64 x)
(- r x)
(-.f64 r x)
x
(+ r x)
(+.f64 x r)
(+ (* 1/2 (/ (pow r 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) r) 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 r (/.f64 r (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 3 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 (pow.f64 r #s(literal 4 binary64)) (fma.f64 (*.f64 (/.f64 r (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 r (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 3 binary64)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) r) r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 r)
(neg.f64 r)
(+ (* -1 (pow x 2)) (pow r 2))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(pow r 2)
(*.f64 r r)
(- (pow r 2) (pow x 2))
(fma.f64 (neg.f64 x) x (*.f64 r r))
-1
#s(literal -1 binary64)
(- (/ (pow r 2) (pow x 2)) 1)
(fma.f64 (/.f64 r x) (/.f64 r x) #s(literal -1 binary64))
(* -1/8 (/ (pow x 4) (pow r 3)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* -1/2 (* (pow r 2) (pow x 2))) (* -1/8 (pow x 4))) (pow r 3))
(/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) r) r (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64))) (pow.f64 r #s(literal 3 binary64)))
(/ (+ (* -1/8 (pow x 4)) (* (pow r 2) (+ (* -1/2 (pow x 2)) (pow r 2)))) (pow r 3))
(/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) (*.f64 r r)) r) r (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64))) (pow.f64 r #s(literal 3 binary64)))
(* -1/8 (/ (pow x 2) (pow r 3)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (*.f64 x x))
(/ (+ (* -1/2 (pow r 2)) (* -1/8 (pow x 2))) (pow r 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 r r) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) (pow.f64 r #s(literal 3 binary64)))
(* -1/8 (/ x (pow r 3)))
(*.f64 (/.f64 x (pow.f64 r #s(literal 3 binary64))) #s(literal -1/8 binary64))
(/ r (pow x 2))
(/.f64 r (*.f64 x x))
(/ -1/8 (pow r 3))
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
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))))))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x r)) 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)))))))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x 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 (fma.f64 (/.f64 (neg.f64 x) r) (/.f64 x r) #s(literal 1 binary64)) r) r)
(* r (+ 1 (* -1 (/ x r))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x r)) r)
(* r (+ 1 (/ x r)))
(fma.f64 (/.f64 x r) r r)
(* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2)))))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x r)) r)
(* r (+ 1 (+ (* -1/2 (/ (pow x 2) (pow r 2))) (* -1/8 (/ (pow x 4) (pow r 4))))))
(*.f64 (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) r) (*.f64 x (/.f64 x r)) #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 #s(literal -1/2 binary64) r) (*.f64 x (/.f64 x r)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/16 binary64)) (pow.f64 r #s(literal 6 binary64))))) r r)
(* (pow r 2) (+ 1 (* -1 (/ (pow x 2) (pow r 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 (neg.f64 x) r) (/.f64 x r) #s(literal 1 binary64)) r) r)
(/ (pow r 2) (pow x 2))
(*.f64 (/.f64 r x) (/.f64 r x))
(* (pow r 2) (- (/ 1 (pow x 2)) (/ 1 (pow r 2))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 r r))) (*.f64 r r))
(/ -1/2 r)
(/.f64 #s(literal -1/2 binary64) r)
(/ (- (* -1/8 (/ (pow x 2) (pow r 2))) 1/2) r)
(fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (*.f64 x x) (/.f64 #s(literal -1/2 binary64) r))
(* -1 (* r (pow (sqrt -1) 2)))
r
(* -1 (* r (+ (* -1/2 (/ (+ x (* -1 x)) r)) (pow (sqrt -1) 2))))
r
(* -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))))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x r)) r)
(* -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))))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x r)) r)
(* (pow r 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) r)) r))))
(*.f64 (*.f64 (fma.f64 (/.f64 (neg.f64 x) r) (/.f64 x r) #s(literal 1 binary64)) r) r)
(* -1 (* r (- (/ x r) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x r)) r)
(* -1 (* r (- (* -1 (/ x r)) 1)))
(fma.f64 (/.f64 x r) r r)
(* -1 (* r (+ 1 (* -1/2 (/ (pow x 2) (pow r 2))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) r) (*.f64 x (/.f64 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)))))))
(*.f64 (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) r) (*.f64 x (/.f64 x r)) #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))) (* -1/16 (/ (pow x 6) (pow r 6))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) r) (*.f64 x (/.f64 x r)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/16 binary64)) (pow.f64 r #s(literal 6 binary64))))) r r))
(* -1 (* r (- (* 1/2 (/ (pow x 2) (pow r 2))) 1)))
(fma.f64 (*.f64 r #s(literal -1/2 binary64)) (*.f64 (/.f64 x r) (/.f64 x r)) r)
(* -1 (* r (- (+ (* 1/8 (/ (pow x 4) (pow r 4))) (* 1/2 (/ (pow x 2) (pow r 2)))) 1)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) r) (*.f64 x (/.f64 x r)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64)) (pow.f64 r #s(literal 4 binary64)))) (neg.f64 r) r)
(* -1 (/ (+ 1/2 (* 1/8 (/ (pow x 2) (pow r 2)))) r))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) r) (*.f64 x (/.f64 x r)) #s(literal 1/2 binary64)) (neg.f64 r))
(+ r (* 1/2 (/ (* x (+ r (* -1 r))) 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)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x 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))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x r) r)
(+ (* x (+ r (* -1 r))) (pow r 2))
(*.f64 r r)
(+ (* x (+ r (+ (* -1 r) (* -1 x)))) (pow r 2))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(+ r (* -1 x))
(-.f64 r x)
(+ r (* -1/2 (/ (pow x 2) r)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x r) r)
(+ r (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))))
(fma.f64 (fma.f64 (/.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)
(+ 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 x (/.f64 x (pow.f64 r #s(literal 5 binary64)))) #s(literal -1/16 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)) (pow x 2))
(fma.f64 (/.f64 r x) (/.f64 r x) #s(literal -1 binary64))
(- (* -1/8 (/ (pow x 2) (pow r 3))) (* 1/2 (/ 1 r)))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (*.f64 x x) (/.f64 #s(literal -1/2 binary64) r))
(* x (+ (sqrt -1) (* 1/2 (/ (+ r (* -1 r)) (* x (sqrt -1))))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* 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)))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (sqrt.f64 #s(literal -1 binary64))) x)
(* 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))))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (sqrt.f64 #s(literal -1 binary64))) x)
(* (pow x 2) (- (+ (* -1 (/ r x)) (/ r x)) 1))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (+ (* -1 (/ r x)) (+ (/ r x) (/ (pow r 2) (pow x 2)))) 1))
(*.f64 (fma.f64 (/.f64 r x) (/.f64 r x) #s(literal -1 binary64)) (*.f64 x x))
(* x (- (/ r x) 1))
(*.f64 (-.f64 (/.f64 r x) #s(literal 1 binary64)) x)
(* x (+ 1 (/ r x)))
(fma.f64 (/.f64 r x) x x)
(* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (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)))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (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))))))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 r #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (/.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)))) x)
(* (pow x 2) (- (/ (pow r 2) (pow x 2)) 1))
(*.f64 (fma.f64 (/.f64 r x) (/.f64 r x) #s(literal -1 binary64)) (*.f64 x x))
(* -1 (* (pow x 4) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(*.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) r))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (/ r (pow x 4)) (+ (* 1/8 (/ 1 (pow r 3))) (/ 1/2 (* r (pow x 2))))))
(*.f64 (-.f64 (/.f64 r (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) r)) (/.f64 #s(literal 1/8 binary64) (pow.f64 r #s(literal 3 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 2) (+ (* 1/8 (/ 1 (pow r 3))) (* 1/2 (/ 1 (* r (pow x 2)))))))
(*.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) r))) (*.f64 x x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ r (* -1 r)) (* x (sqrt -1)))))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -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 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 r (/.f64 r (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) #s(literal 0 binary64)) x)) 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 (/.f64 (/.f64 (fma.f64 (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) x) x) (sqrt.f64 #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 r x) (/.f64 r x) #s(literal -1 binary64)) (*.f64 x x))
(* -1 (* x (+ 1 (* -1 (/ r x)))))
(*.f64 (-.f64 (/.f64 r x) #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (/ r x)) 1)))
(fma.f64 (/.f64 r x) x x)
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1)))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (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)))) (* 1/2 (/ (pow r 2) (* (pow x 2) (sqrt -1))))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 r (/.f64 r (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 r #s(literal 4 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 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)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 r x) (/.f64 r x)) (/.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))

rewrite195.0ms (5.2%)

Memory
-4.0MiB live, 70.8MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035187
060187
1223187
21570183
08614183
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 1 133
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
(*.f64 (-.f64 r x) (+.f64 x r))
(-.f64 r x)
(+.f64 x r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
(neg.f64 r)
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
(fma.f64 (neg.f64 x) x (*.f64 r r))
(neg.f64 x)
(*.f64 r r)
(*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x))
(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))))
#s(approx (- (pow r 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64)) (*.f64 x x)))
(fma.f64 (/.f64 (/.f64 r x) x) r #s(literal -1 binary64))
(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)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
(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 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))) x)
(/.f64 (/.f64 r x) x)
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
Outputs
(*.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (hypot.f64 x r)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 r #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (fma.f64 x x (*.f64 r r)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 r #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 r) r)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 r #s(literal 3/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) x) (pow.f64 r #s(literal -3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 r (*.f64 (/.f64 #s(literal -1/8 binary64) r) (/.f64 x r))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 r r) (/.f64 (*.f64 #s(literal -1/8 binary64) x) r)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)) (*.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (neg.f64 r) #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)) (*.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (neg.f64 r) #s(literal 3 binary64)) (*.f64 x #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 r #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 r #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 r #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) x))))
(/.f64 (neg.f64 x) (neg.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64))))
(/.f64 x (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)))
(exp.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) r)) #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) r)) #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 r x) (sqrt.f64 x)))
(*.f64 (/.f64 (neg.f64 r) (sqrt.f64 x)) (/.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (/.f64 r (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 r x) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 r (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 r) x) (/.f64 (sqrt.f64 r) x))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 (neg.f64 r) x) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 r x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (neg.f64 r) x))
(*.f64 (/.f64 r #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) x))
(*.f64 (/.f64 r #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 x (neg.f64 r)) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (*.f64 r #s(literal 1 binary64)) (pow.f64 x #s(literal -2 binary64)))
(*.f64 (*.f64 (neg.f64 r) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 r #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 r x))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 r x) x))
(*.f64 (/.f64 (neg.f64 r) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (neg.f64 r) x) (/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 r) x) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (*.f64 x x) r))))
(*.f64 (/.f64 r x) (/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 r x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (neg.f64 r) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(*.f64 r (pow.f64 x #s(literal -2 binary64)))
(pow.f64 (/.f64 (*.f64 x x) r) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 r) #s(literal 1 binary64))) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (*.f64 r #s(literal 1 binary64))) (*.f64 (neg.f64 x) x))
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 x r)))
(/.f64 (*.f64 r #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (neg.f64 (neg.f64 r)) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (*.f64 (neg.f64 r) #s(literal 1 binary64)) (*.f64 (neg.f64 x) x))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x r))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 x) x) (*.f64 (neg.f64 r) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 r #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) r))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) r))
(/.f64 (/.f64 (neg.f64 r) x) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 (neg.f64 r) x) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) r)))
(/.f64 (/.f64 r x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 r x) x)
(/.f64 (neg.f64 r) (*.f64 (neg.f64 x) x))
(/.f64 r (*.f64 x x))
(neg.f64 (/.f64 (/.f64 (neg.f64 r) x) x))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (neg.f64 (neg.f64 x))) (/.f64 (/.f64 (neg.f64 r) x) x))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) x) (/.f64 (/.f64 (neg.f64 r) x) x))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x)) (/.f64 r (*.f64 (neg.f64 x) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (/.f64 (neg.f64 r) x) x))
(exp.f64 (-.f64 (log.f64 r) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) r)) #s(literal -1 binary64)))
(*.f64 (pow.f64 r #s(literal -3/2 binary64)) (pow.f64 (*.f64 (pow.f64 r #s(literal 3/2 binary64)) #s(literal -8 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 r #s(literal -2 binary64)) (pow.f64 (*.f64 r #s(literal -8 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 r #s(literal -2 binary64)) #s(literal -3/2 binary64)) (pow.f64 (*.f64 r #s(literal -2 binary64)) #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3/2 binary64))) (pow.f64 r #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 r r)) (pow.f64 r #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1/8 binary64) r) (pow.f64 r #s(literal -2 binary64)))
(*.f64 (pow.f64 r #s(literal -3 binary64)) #s(literal -1/8 binary64))
(*.f64 (pow.f64 r #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 r r) #s(literal -8 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) r) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) r))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 (neg.f64 r) #s(literal -1 binary64)) #s(literal 3 binary64)))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 (neg.f64 r) #s(literal 3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1/2 binary64) r) (pow.f64 (/.f64 #s(literal -1/2 binary64) r) #s(literal 2 binary64)))
(*.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal -3 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)))))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) r))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 r #s(literal -2 binary64)) #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 r #s(literal -2 binary64)) #s(literal -3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) r) #s(literal 2 binary64)) #s(literal 3/2 binary64))
(pow.f64 (/.f64 #s(literal -1/2 binary64) r) #s(literal 3 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3/2 binary64)))) (neg.f64 (pow.f64 r #s(literal 3/2 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 r r))) (neg.f64 r))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) r)) (neg.f64 (*.f64 r r)))
(/.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3/2 binary64))) (pow.f64 r #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 r r)) r)
(/.f64 (/.f64 #s(literal -1/8 binary64) r) (*.f64 r r))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 r #s(literal 3/2 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 r (/.f64 #s(literal -1/8 binary64) (*.f64 r r))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 r r) (/.f64 #s(literal -1/8 binary64) r)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64)))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 (pow.f64 (neg.f64 r) #s(literal 3 binary64)))))
(/.f64 #s(literal 1/8 binary64) (pow.f64 (neg.f64 r) #s(literal 3 binary64)))
(/.f64 #s(literal -1/8 binary64) (pow.f64 (neg.f64 (neg.f64 r)) #s(literal 3 binary64)))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (pow.f64 (neg.f64 r) #s(literal 3 binary64))))
(/.f64 #s(literal -1/8 binary64) (pow.f64 r #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (*.f64 r #s(literal -2 binary64))) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64))))
(neg.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) r) #s(literal 3 binary64)))
(neg.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 r #s(literal -3 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 r #s(literal 3 binary64)) #s(literal -8 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) r)) #s(literal 3 binary64)))

eval139.0ms (3.7%)

Memory
9.4MiB live, 94.4MiB allocated
Compiler

Compiled 28 367 to 3 928 computations (86.2% saved)

prune20.0ms (0.5%)

Memory
-40.7MiB live, 37.0MiB allocated
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New9236929
Fresh123
Picked325
Done000
Total92710937
Accuracy
100.0%
Counts
937 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (*.f64 r r)))))
99.4%
(*.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) r (*.f64 (+.f64 x r) (neg.f64 x))))
✓99.8%
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 r r)))
✓99.8%
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
99.7%
(sqrt.f64 (*.f64 (-.f64 r x) #s(approx (+ x r) (fma.f64 (/.f64 r x) x x))))
99.7%
(sqrt.f64 #s(approx (+ (* (neg x) x) (* r r)) (*.f64 (*.f64 (fma.f64 (/.f64 (neg.f64 x) r) (/.f64 x r) #s(literal 1 binary64)) r) r)))
82.6%
#s(approx (sqrt (- (pow r 2) (pow x 2))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) r) x) x r))
64.9%
#s(approx (sqrt (* (- r x) (+ x r))) r)
Compiler

Compiled 327 to 166 computations (49.2% saved)

regimes22.0ms (0.6%)

Memory
15.6MiB live, 15.6MiB allocated
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (* (- r x) (+ 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 (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) r (*.f64 (+.f64 x r) (neg.f64 x))))
(*.f64 (sqrt.f64 (-.f64 r x)) (sqrt.f64 (+.f64 x r)))
(sqrt.f64 (*.f64 (-.f64 r x) #s(approx (+ x r) (fma.f64 (/.f64 r x) x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (*.f64 r 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 #s(approx (+ (* (neg x) x) (* r r)) (*.f64 (*.f64 (fma.f64 (/.f64 (neg.f64 x) r) (/.f64 x r) #s(literal 1 binary64)) r) r)))
(sqrt.f64 (fma.f64 (pow.f64 r #s(literal 3/2 binary64)) (sqrt.f64 r) (*.f64 (neg.f64 x) x)))
#s(approx (sqrt (- (pow r 2) (pow x 2))) (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))
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Outputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
Calls

6 calls:

4.0ms
r
3.0ms
(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (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 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)

regimes8.0ms (0.2%)

Memory
9.6MiB live, 9.6MiB allocated
Accuracy

Total -40.5b remaining (-180.1%)

Threshold costs -40.5b (-180.1%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (* (- r x) (+ x r))) r)
#s(approx (sqrt (- (pow r 2) (pow x 2))) (neg.f64 r))
Outputs
#s(approx (sqrt (* (- r x) (+ 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 x #s(literal 2 binary64))
1.0ms
(pow.f64 r #s(literal 2 binary64))
1.0ms
x
Results
AccuracySegmentsBranch
64.9%1r
64.9%1x
64.9%1(sqrt.f64 (-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
64.9%1(-.f64 (pow.f64 r #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
64.9%1(pow.f64 r #s(literal 2 binary64))
64.9%1(pow.f64 x #s(literal 2 binary64))
Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify50.0ms (1.3%)

Memory
10.8MiB live, 10.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01118
12318
25218
311018
420318
542718
6102218
7359518
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (sqrt (* (- r x) (+ x r))) r)
Outputs
(sqrt.f64 (*.f64 (-.f64 r x) (+.f64 x r)))
#s(approx (sqrt (* (- r x) (+ x r))) r)

soundness233.0ms (6.1%)

Memory
5.5MiB live, 5.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03971586
112561206
255061146
083641081
0721
01121
14221
224321
3215821
0924921
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 51 to 35 computations (31.4% saved)

preprocess19.0ms (0.5%)

Memory
12.7MiB live, 12.7MiB allocated
Remove

(abs r)

(abs x)

Compiler

Compiled 84 to 60 computations (28.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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