sin(x)*sin(x)+cos(x)*cos(x)

Time bar (total: 2.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.4%49.6%0%0%0%0
100%50.4%0%49.6%0%0%0%1
Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.0s (52.6%)

Memory
27.3MiB live, 522.2MiB allocated
Samples
581.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 407.0ms
ival-mult: 107.0ms (26.3% of total)
ival-<=: 82.0ms (20.2% of total)
ival-sin: 74.0ms (18.2% of total)
ival-cos: 66.0ms (16.2% of total)
ival-add: 49.0ms (12.1% of total)
ival-and: 14.0ms (3.4% of total)
exact: 11.0ms (2.7% of total)
ival-assert: 3.0ms (0.7% of total)
Bogosity

explain104.0ms (5.3%)

Memory
-10.2MiB live, 65.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
00-0-(*.f64 (sin.f64 x) (sin.f64 x))
00-0-(cos.f64 x)
00-0-(*.f64 (cos.f64 x) (cos.f64 x))
00-0-(sin.f64 x)
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
53.0ms512×0valid
Compiler

Compiled 67 to 22 computations (67.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-sin: 27.0ms (68% of total)
ival-mult: 6.0ms (15.1% of total)
ival-cos: 4.0ms (10.1% of total)
ival-add: 2.0ms (5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess14.0ms (0.7%)

Memory
5.1MiB live, 5.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
1212
2512
3832
41222
51452
61582
71632
81692
91692
0611
01111
1121
2131
3151
0151
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Outputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
#s(literal 1 binary64)
Symmetry

(abs x)

Compiler

Compiled 11 to 6 computations (45.5% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Compiler

Compiled 11 to 6 computations (45.5% saved)

simplify3.0ms (0.1%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (cos.f64 x) (cos.f64 x))
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 (sin.f64 x) (sin.f64 x))
cost-diff10
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0626
01126
11216
21316
31516
01516
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
(*.f64 (sin.f64 x) (sin.f64 x))
(sin.f64 x)
x
(*.f64 (cos.f64 x) (cos.f64 x))
(cos.f64 x)
Outputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
#s(literal 1 binary64)
(*.f64 (sin.f64 x) (sin.f64 x))
(sin.f64 x)
x
(*.f64 (cos.f64 x) (cos.f64 x))
(cos.f64 x)

localize20.0ms (1%)

Memory
7.8MiB live, 7.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sin.f64 x)
accuracy0.0
(cos.f64 x)
accuracy0.01953125
(*.f64 (sin.f64 x) (sin.f64 x))
accuracy0.01953125
(*.f64 (cos.f64 x) (cos.f64 x))
Samples
14.0ms256×0valid
Compiler

Compiled 28 to 8 computations (71.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 3.0ms (36.8% of total)
ival-cos: 2.0ms (24.5% of total)
ival-sin: 2.0ms (24.5% of total)
ival-add: 1.0ms (12.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.2%)

Memory
1.5MiB live, 1.5MiB allocated
Counts
5 → 20
Calls
Call 1
Inputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
(*.f64 (sin.f64 x) (sin.f64 x))
(sin.f64 x)
(*.f64 (cos.f64 x) (cos.f64 x))
(cos.f64 x)
Outputs
1
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (pow (cos x) 2) (pow (sin x) 2))
(pow (sin x) 2)
(sin x)
(pow (cos x) 2)
(cos x)
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@0
((+ (* (sin x) (sin x)) (* (cos x) (cos x))) (* (sin x) (sin x)) (sin x) (* (cos x) (cos x)) (cos x))
1.0ms
x
@inf
((+ (* (sin x) (sin x)) (* (cos x) (cos x))) (* (sin x) (sin x)) (sin x) (* (cos x) (cos x)) (cos x))
1.0ms
x
@-inf
((+ (* (sin x) (sin x)) (* (cos x) (cos x))) (* (sin x) (sin x)) (sin x) (* (cos x) (cos x)) (cos x))

simplify157.0ms (8%)

Memory
37.0MiB live, 37.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077191
1190190
2464174
31472174
42802174
54265174
65345174
77241174
08075153
Stop Event
1×iter limit
1×node limit
Counts
20 → 19
Calls
Call 1
Inputs
1
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (pow (cos x) 2) (pow (sin x) 2))
(pow (sin x) 2)
(sin x)
(pow (cos x) 2)
(cos x)
Outputs
1
#s(literal 1 binary64)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 x x) #s(literal 2/45 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x #s(literal -1 binary64)))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (pow (cos x) 2) (pow (sin x) 2))
#s(literal 1 binary64)
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin x)
(sin.f64 x)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos x)
(cos.f64 x)

rewrite198.0ms (10.1%)

Memory
-19.5MiB live, 58.8MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0625
01121
14513
239813
3665113
0840713
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 277
Calls
Call 1
Inputs
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
(*.f64 (sin.f64 x) (sin.f64 x))
(sin.f64 x)
(*.f64 (cos.f64 x) (cos.f64 x))
(cos.f64 x)
Outputs
#s(literal 1 binary64)
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -2 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (sin.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))
(*.f64 (exp.f64 (log.f64 (sin.f64 x))) (exp.f64 (log.f64 (sin.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))))
(*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal -2 binary64) (/.f64 (*.f64 (sin.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(*.f64 #s(literal -2 binary64) (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (sin.f64 x))
(pow.f64 (exp.f64 (log.f64 (sin.f64 x))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (cos.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))
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(fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/4 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 4 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (cos.f64 x) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (cos.f64 x) (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 x) (*.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (cos.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)))
(fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 0 binary64))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 (cos.f64 x) (sin.f64 x))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) #s(literal 1 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(-.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(exp.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(+.f64 (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(+.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(+.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64))))
(+.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))
(+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(+.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))

eval33.0ms (1.7%)

Memory
27.9MiB live, 27.9MiB allocated
Compiler

Compiled 6 476 to 914 computations (85.9% saved)

prune4.0ms (0.2%)

Memory
11.1MiB live, 11.1MiB allocated
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New3101311
Fresh000
Picked101
Done000
Total3111312
Accuracy
100.0%
Counts
312 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify3.0ms (0.2%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0814
0814
1114
2124
0124
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
#s(literal 1 binary64)

localize21.0ms (1.1%)

Memory
-71.9MiB live, 6.7MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy0.0
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Samples
16.0ms256×0valid
Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 3.0ms (34.3% of total)
ival-cos: 2.0ms (22.8% of total)
ival-sin: 2.0ms (22.8% of total)
ival-add: 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)

series1.0ms (0.1%)

Memory
0.7MiB live, 0.7MiB allocated
Counts
1 → 2
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Outputs
1
(+ (pow (cos x) 2) (pow (sin x) 2))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((+ (* (sin x) (sin x)) (* (cos x) (cos x))))
0.0ms
x
@inf
((+ (* (sin x) (sin x)) (* (cos x) (cos x))))
0.0ms
x
@-inf
((+ (* (sin x) (sin x)) (* (cos x) (cos x))))

simplify2.0ms (0.1%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082
1132
2132
0132
Stop Event
1×iter limit
1×saturated
Counts
2 → 2
Calls
Call 1
Inputs
1
(+ (pow (cos x) 2) (pow (sin x) 2))
Outputs
1
#s(literal 1 binary64)
(+ (pow (cos x) 2) (pow (sin x) 2))
#s(literal 1 binary64)

rewrite157.0ms (8%)

Memory
47.3MiB live, 47.3MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
0811
1433
23953
366513
084073
Stop Event
1×iter limit
1×node limit
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Outputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 13 to 8 computations (38.5% saved)

prune1.0ms (0.1%)

Memory
0.7MiB live, 0.7MiB allocated
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New101
Fresh000
Picked011
Done000
Total112
Accuracy
100.0%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Compiler

Compiled 37 to 21 computations (43.2% saved)

regimes2.0ms (0.1%)

Memory
2.7MiB live, 2.7MiB allocated
Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Outputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Calls

2 calls:

1.0ms
x
1.0ms
(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))
Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify9.0ms (0.5%)

Memory
6.2MiB live, 6.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
1113
2123
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))
Outputs
#s(approx (+ (* (sin x) (sin x)) (* (cos x) (cos x))) #s(literal 1 binary64))

soundness185.0ms (9.4%)

Memory
0.4MiB live, 0.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077191
1190190
2464174
31472174
42802174
54265174
65345174
77241174
08075153
Stop Event
1×done
1×iter limit
1×node limit
Compiler

Compiled 14 to 10 computations (28.6% saved)

preprocess12.0ms (0.6%)

Memory
8.9MiB live, 8.9MiB allocated
Remove

(abs x)

Compiler

Compiled 74 to 44 computations (40.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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