tanhf (example 3.4)

Time bar (total: 5.2s)

analyze119.0ms (2.3%)

Algorithm
1×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)

sample4.2s (81.4%)

Results
2.4s2078×body2048valid
1.1s4618×body256valid
372.0ms1026×body1024valid
233.0ms461×body512valid
53.0ms73×body4096valid
Bogosity

preprocess214.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
750×fma-def
410×div-sub
196×associate-/r*
176×associate-/l*
118×sub-neg
Problems
109×No Errors
81×(-.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
1×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)

eval0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(tan.f64 (/.f64 x 2))
▶100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 10 to 8 computations (20% saved)

localize30.0ms (0.6%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 11 to 8 computations (27.3% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(tan.f64 (/.f64 x 2))
1.0ms
x
@-inf
(tan.f64 (/.f64 x 2))
1.0ms
x
@0
(tan.f64 (/.f64 x 2))

rewrite177.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
1294×frac-times
400×unpow-prod-down
328×cbrt-prod
324×log-prod
313×log1p-expm1-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
17614
287014
Stop Event
1×node limit
Counts
1 → 46
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
Outputs
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2)))) 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 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (log.f64 (E.f64)))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.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 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sin.f64 (*.f64 x 1/2)))) (cbrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (tan.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(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)) 2) 1/2)
(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 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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 (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))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

simplify61.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
928×associate-*r*
804×associate-*l*
734×associate-+r+
734×associate-+l+
676×fma-def
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01471671
12941608
28301586
343571586
Stop Event
1×node limit
Counts
58 → 78
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)))
(+.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))))
(/.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 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2)))) 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 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (log.f64 (E.f64)))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.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 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sin.f64 (*.f64 x 1/2)))) (cbrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (tan.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(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)) 2) 1/2)
(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 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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 (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))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
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))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/2 x)))
(+.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)))))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (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 0 (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(+.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))))))
(tan.f64 (*.f64 1/2 x))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 x 1/2)) (log.f64 (E.f64)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(*.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 5)))
(*.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 5/2))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(tan.f64 (/.f64 (-.f64 (+.f64 x 1) 1) 2))
(tan.f64 (/.f64 (+.f64 x 0) 2))
(tan.f64 (/.f64 x 2))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sin.f64 (*.f64 x 1/2)))) (cbrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (cbrt.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))) (cbrt.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))) (sqrt.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sqrt.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (tan.f64 (*.f64 x 1/2)))) (sqrt.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x)))) (sqrt.f64 (cos.f64 (*.f64 1/2 x))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) -1)
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(neg.f64 (tan.f64 (*.f64 1/2 x)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(tan.f64 (*.f64 1/2 x))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) 2))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))

eval25.0ms (0.5%)

Compiler

Compiled 888 to 741 computations (16.6% saved)

prune12.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New77178
Fresh000
Picked011
Done000
Total77279
Accuracy
100.0%
Counts
79 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.3%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
▶52.3%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize16.0ms (0.3%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accuracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓52.3%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 24 to 18 computations (25% saved)

regimes17.0ms (0.3%)

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:

4.0ms
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:

3.0ms
x
Results
AccuracySegmentsBranch
52.3%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
11224
Stop Event
1×done
1×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)

soundness229.0ms (4.4%)

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
1×saturated
Compiler

Compiled 12 to 9 computations (25% saved)

end0.0ms (0%)

preprocess48.0ms (0.9%)

Remove

(negabs x)

Compiler

Compiled 72 to 56 computations (22.2% saved)

Profiling

Loading profile data...