tanhf (example 3.4)

Time bar (total: 4.7s)

analyze132.0ms (2.8%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
37.5%37.5%62.5%0%0%0%0%4
43.8%43.7%56.2%0%0%0%0%5
46.9%46.9%53.1%0%0%0%0%6
48.4%48.4%51.5%0%0%0%0%7
49.2%49.2%50.8%0%0%0%0%8
49.6%49.6%50.4%0%0%0%0%9
49.8%49.8%50.2%0%0%0%0%10
49.9%49.9%50.1%0%0%0%0%11
50%49.9%50%0%0%0%0%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions
Click to see histograms
Operation ival-sub, total time spent: 16.0ms
Operation ival-sin, total time spent: 8.0ms
Operation ival-div, total time spent: 9.0ms
Operation ival-cos, total time spent: 9.0ms
Operation const, total time spent: 3.0ms

sample3.5s (73.9%)

Results
1.5s2270×body3valid
1.2s4489×body0valid
631.0ms1274×body2valid
63.0ms216×body1valid
12.0msbody5valid
Precisions
Click to see histograms
Operation ival-sub, total time spent: 124.0ms
Operation ival-sin, total time spent: 302.0ms
Operation ival-div, total time spent: 198.0ms
Operation ival-cos, total time spent: 1023.0ms
Operation const, total time spent: 31.0ms
Bogosity

preprocess210.0ms (4.4%)

Algorithm
egg-herbie
Rules
750×fma-def
410×div-sub
196×associate-/r*
176×associate-/l*
118×sub-neg
Problems
110×No Errors
80×(-.f64 1 (cos.f64 x))
66×(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01760
14460
26956
314356
432656
573456
6139356
7177756
8185856
9193556
10198656
11199856
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(tan.f64 (/.f64 (neg.f64 x) 2))
(tan.f64 (*.f64 -1/2 x))
(tan.f64 (*.f64 x -1/2))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
Symmetry

(negabs x)

Compiler

Compiled 27 to 16 computations (40.7% saved)

Precisions
Click to see histograms
Operation ival-sub, total time spent: 8.0ms
Operation ival-sin, total time spent: 10.0ms
Operation ival-div, total time spent: 5.0ms
Operation ival-cos, total time spent: 29.0ms
Operation const, total time spent: 2.0ms

eval0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
100.0%
(tan.f64 (/.f64 x 2))
50.6%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize171.0ms (3.6%)

Localize:

Found 3 expressions with local error:

NewAccuracyProgram
75.8%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
75.2%
(-.f64 1 (cos.f64 x))
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 28 to 16 computations (42.9% saved)

Precisions
Click to see histograms
Operation ival-tan, total time spent: 26.0ms
Operation ival-sub, total time spent: 8.0ms
Operation ival-sin, total time spent: 9.0ms
Operation ival-div, total time spent: 15.0ms
Operation ival-cos, total time spent: 28.0ms
Operation const, total time spent: 3.0ms

series4.0ms (0.1%)

Counts
3 → 20
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(tan.f64 (/.f64 x 2))
1.0ms
x
@-inf
(tan.f64 (/.f64 x 2))
1.0ms
x
@0
(-.f64 1 (cos.f64 x))
0.0ms
x
@0
(tan.f64 (/.f64 x 2))
0.0ms
x
@inf
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

rewrite272.0ms (5.8%)

Algorithm
batch-egg-rewrite
Rules
833×log1p-expm1-u
833×expm1-log1p-u
772×log-prod
452×prod-diff
342×pow-prod-up
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01442
116642
2216342
Stop Event
node limit
Counts
3 → 239
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
(-.f64 1 (cos.f64 x))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(+.f64 (tan.f64 (*.f64 x 1/2)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(+.f64 (tan.f64 (*.f64 x 1/2)) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 1 (tan.f64 x))))
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (/.f64 1 (sin.f64 x)) (neg.f64 (/.f64 1 (tan.f64 x))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 1 (tan.f64 x)) 1))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 x))) 1 (*.f64 (/.f64 1 (tan.f64 x)) 1)))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (sin.f64 x))) (cos.f64 x) (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x)))) (/.f64 1 (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) 1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1))))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (tan.f64 x)) 1))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 x))) 1 (*.f64 (/.f64 1 (tan.f64 x)) 1)))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (sin.f64 x))) (cos.f64 x) (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x)))) (/.f64 1 (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) 1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (tan.f64 x)) 1))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 x))) 1 (*.f64 (/.f64 1 (tan.f64 x)) 1)))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (sin.f64 x))) (cos.f64 x) (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
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(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (log.f64 (exp.f64 1)))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (/.f64 x -2))))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (neg.f64 (sin.f64 x))))
(*.f64 (/.f64 1 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (sin.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sin.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (sqrt.f64 (sin.f64 x))) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (sin.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sin.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (sin.f64 x))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(pow.f64 (/.f64 (cos.f64 (/.f64 x -2)) (sin.f64 (*.f64 x 1/2))) -1)
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) 2)))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (sin.f64 x) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) 2))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (/.f64 1 (tan.f64 x))))
(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))
(fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))

simplify171.0ms (3.6%)

Algorithm
egg-herbie
Rules
1102×unswap-sqr
572×cancel-sign-sub-inv
550×div-sub
450×distribute-lft-neg-in
428×distribute-rgt-neg-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
046120332
1111514759
238547131
Stop Event
node limit
Counts
259 → 206
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
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(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) 1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1))))
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (tan.f64 x)) 1))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 x))) 1 (*.f64 (/.f64 1 (tan.f64 x)) 1)))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (sin.f64 x))) (cos.f64 x) (*.f64 (/.f64 1 (sin.f64 x)) (cos.f64 x))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (*.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) (cbrt.f64 (/.f64 1 (tan.f64 x)))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x)))) (/.f64 1 (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cos.f64 x) (sqrt.f64 (sin.f64 x))) (/.f64 1 (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (sqrt.f64 (sin.f64 x))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) 1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 x)) (/.f64 (sqrt.f64 (cos.f64 x)) 1))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (*.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (cbrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (log.f64 (exp.f64 1)))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (/.f64 x -2))))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(*.f64 (neg.f64 (-.f64 1 (cos.f64 x))) (/.f64 1 (neg.f64 (sin.f64 x))))
(*.f64 (/.f64 1 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (sin.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sin.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (sqrt.f64 (sin.f64 x))) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (sin.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sin.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (sin.f64 x))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(pow.f64 (/.f64 (cos.f64 (/.f64 x -2)) (sin.f64 (*.f64 x 1/2))) -1)
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) 2)))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (sin.f64 x) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) 2))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (/.f64 1 (tan.f64 x))))
(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))
(fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 17/40320 (pow.f64 x 7)) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 -1/40320 (pow.f64 x 8)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6)))))
(*.f64 1/2 x)
(+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 17/40320 (pow.f64 x 7)) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))))
(+.f64 (tan.f64 (*.f64 x 1/2)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(+.f64 (tan.f64 (*.f64 x 1/2)) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))) (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (sin.f64 x))) (/.f64 1 (tan.f64 x))))
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(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 (cos.f64 (/.f64 x -2)) (sin.f64 (*.f64 x 1/2))) -1)
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (/.f64 x -2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (/.f64 x -2)))
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) 2)))
(+.f64 (fma.f64 1 (/.f64 1 (sin.f64 x)) (*.f64 (/.f64 -1 (sin.f64 x)) (cos.f64 x))) (fma.f64 (/.f64 -1 (sin.f64 x)) (cos.f64 x) (*.f64 (cos.f64 x) (/.f64 1 (sin.f64 x)))))
(+.f64 (*.f64 0 (/.f64 (cos.f64 x) (sin.f64 x))) (tan.f64 (/.f64 x 2)))
(tan.f64 (/.f64 x 2))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (sin.f64 x) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 (*.f64 x 1/2))) 1) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) 2))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(tan.f64 (*.f64 x 1/2))
(+.f64 (tan.f64 (*.f64 1/2 x)) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (tan.f64 x)))) (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (tan.f64 x))))
(tan.f64 (*.f64 1/2 x))
(fma.f64 1 (/.f64 1 (sin.f64 x)) (neg.f64 (/.f64 1 (tan.f64 x))))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 x)))
(+.f64 (/.f64 1 (sin.f64 x)) (/.f64 -1 (tan.f64 x)))
(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (cbrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 x)))
(+.f64 (/.f64 1 (sin.f64 x)) (/.f64 -1 (tan.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (sqrt.f64 (/.f64 1 (sin.f64 x))) (neg.f64 (/.f64 1 (tan.f64 x))))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 x)))
(+.f64 (/.f64 1 (sin.f64 x)) (/.f64 -1 (tan.f64 x)))

eval65.0ms (1.4%)

Compiler

Compiled 4097 to 2253 computations (45% saved)

prune25.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2051206
Fresh000
Picked022
Done000
Total2053208
Accuracy
100.0%
Counts
208 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
53.4%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
50.6%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
53.4%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 34 to 26 computations (23.5% saved)

localize19.0ms (0.4%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions
Click to see histograms
Operation ival-mult, total time spent: 3.0ms
Operation const, total time spent: 1.0ms

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033
Accuracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
53.4%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 32 to 24 computations (25% saved)

regimes7.0ms (0.1%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 1/2 x)
(tan.f64 (/.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(tan.f64 (/.f64 x 2))
Calls

2 calls:

3.0ms
x
3.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 25 to 18 computations (28% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
53.4%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
11224
Stop Event
done
saturated
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
Outputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
(*.f64 x 1/2)
Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness115.0ms (2.4%)

Rules
750×fma-def
410×div-sub
196×associate-/r*
176×associate-/l*
118×sub-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01760
14460
26956
314356
432656
573456
6139356
7177756
8185856
9193556
10198656
11199856
Stop Event
saturated
Compiler

Compiled 12 to 9 computations (25% saved)

end0.0ms (0%)

preprocess34.0ms (0.7%)

Remove

(negabs x)

Compiler

Compiled 72 to 56 computations (22.2% saved)

Profiling

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