tanhf (example 3.4)

Details

Time bar (total: 5.6s)

analyze156.0ms (2.8%)

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)

sample4.7s (83%)

Results
2.5s2092×body2048valid
1.4s3138×body1024valid
405.0ms1502×body512valid
239.0ms1408×body256valid
120.0ms116×body4096valid
Bogosity

preprocess31.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify26.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))

eval1.0ms (0%)

Compiler

Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Accurracy
100.0%
Counts
3 → 1
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)

localize37.0ms (0.7%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiled 11 to 8 computations (27.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite53.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
1366×pow1
1262×add-exp-log
1262×log1p-expm1-u
1262×expm1-log1p-u
1234×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114811
2172411
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
Outputs
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.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)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

simplify70.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1072×log-prod
980×fma-def
832×fma-neg
742×exp-prod
496×exp-sum
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068804
1144708
2438612
32071612
44553612
56569612
Stop Event
1×node limit
Counts
32 → 36
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.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 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.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)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/2 x)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(/.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 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(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))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(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))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(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 (/.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 (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 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval15.0ms (0.3%)

Compiler

Compiled 350 to 283 computations (19.1% saved)

prune6.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New34236
Fresh000
Picked011
Done000
Total34337
Accurracy
100.0%
Counts
37 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.7%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
▶65.4%
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
▶53.7%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
▶65.4%
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
Compiler

Compiled 34 to 28 computations (17.6% saved)

localize227.0ms (4%)

Local Accuracy

Found 3 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(tan.f64 (*.f64 x 1/2))
✓99.4%
(pow.f64 (tan.f64 (*.f64 x 1/2)) 3)
✓65.4%
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
Compiler

Compiled 30 to 23 computations (23.3% saved)

series2.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(pow.f64 (tan.f64 (*.f64 x 1/2)) 3)
1.0ms
x
@-inf
(pow.f64 (tan.f64 (*.f64 x 1/2)) 3)
0.0ms
x
@0
(pow.f64 (tan.f64 (*.f64 x 1/2)) 3)
0.0ms
x
@0
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
0.0ms
x
@inf
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))

rewrite83.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
1608×pow1
1496×add-exp-log
1494×log1p-expm1-u
1494×expm1-log1p-u
1466×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
120739
2209639
Stop Event
1×node limit
Counts
3 → 70
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 3)
(tan.f64 (*.f64 x 1/2))
Outputs
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3))
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(-.f64 (+.f64 1 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1)
(*.f64 1 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (tan.f64 (*.f64 x 1/2)))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) 3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 3) (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 3))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1) (tan.f64 (*.f64 x 1/2)))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) (pow.f64 (cos.f64 (*.f64 x 1/2)) 3))
(/.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)) (cos.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 6))
(log.f64 (exp.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(cbrt.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(exp.f64 (log.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(log1p.f64 (expm1.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3))
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

simplify84.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
2064×fma-def
1090×distribute-rgt-in
1040×distribute-lft-in
664×associate-/l*
610×associate-/r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01362928
13072574
29672220
332252166
Stop Event
1×node limit
Counts
106 → 85
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.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 1/8 (pow.f64 x 3))
(+.f64 (*.f64 1/32 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3)))
(+.f64 (*.f64 11/1920 (pow.f64 x 7)) (+.f64 (*.f64 1/32 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3))))
(+.f64 (*.f64 11/1920 (pow.f64 x 7)) (+.f64 (*.f64 1/32 (pow.f64 x 5)) (+.f64 (*.f64 11/12096 (pow.f64 x 9)) (*.f64 1/8 (pow.f64 x 3)))))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.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 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3))
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(-.f64 (+.f64 1 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1)
(*.f64 1 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (tan.f64 (*.f64 x 1/2)))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)))
(*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) 3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 3) (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 3))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1) (tan.f64 (*.f64 x 1/2)))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sqrt.f64 (tan.f64 (*.f64 x 1/2)))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) (pow.f64 (cos.f64 (*.f64 x 1/2)) 3))
(/.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)) (cos.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 6))
(log.f64 (exp.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(cbrt.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(exp.f64 (log.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(log1p.f64 (expm1.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.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 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3))
(*.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 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 x 1/2)))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2) 1/3))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(*.f64 x (fma.f64 1/24 (*.f64 x x) 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(fma.f64 x (fma.f64 1/24 (*.f64 x x) 1/2) (*.f64 1/240 (pow.f64 x 5)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 1/24 (*.f64 x x) 1/2) (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7))))
(/.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 1/8 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) 1/8)
(+.f64 (*.f64 1/32 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3)))
(fma.f64 1/32 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/8))
(fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 5) 1/32))
(+.f64 (*.f64 11/1920 (pow.f64 x 7)) (+.f64 (*.f64 1/32 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3))))
(fma.f64 11/1920 (pow.f64 x 7) (fma.f64 1/32 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/8)))
(fma.f64 (pow.f64 x 7) 11/1920 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 5) 1/32)))
(fma.f64 (pow.f64 x 5) 1/32 (fma.f64 (pow.f64 x 7) 11/1920 (*.f64 (pow.f64 x 3) 1/8)))
(+.f64 (*.f64 11/1920 (pow.f64 x 7)) (+.f64 (*.f64 1/32 (pow.f64 x 5)) (+.f64 (*.f64 11/12096 (pow.f64 x 9)) (*.f64 1/8 (pow.f64 x 3)))))
(fma.f64 11/1920 (pow.f64 x 7) (fma.f64 1/32 (pow.f64 x 5) (fma.f64 11/12096 (pow.f64 x 9) (*.f64 (pow.f64 x 3) 1/8))))
(fma.f64 (pow.f64 x 7) 11/1920 (fma.f64 (pow.f64 x 5) 1/32 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 11/12096 (pow.f64 x 9)))))
(fma.f64 (pow.f64 x 5) 1/32 (fma.f64 (pow.f64 x 7) 11/1920 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 11/12096 (pow.f64 x 9)))))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3))
(pow.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3)
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(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval26.0ms (0.5%)

Compiler

Compiled 1025 to 848 computations (17.3% saved)

prune13.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New85085
Fresh000
Picked022
Done011
Total85388
Accurracy
100.0%
Counts
88 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓53.7%
(*.f64 1/2 x)
✓100.0%
(tan.f64 (/.f64 x 2))
✓65.4%
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
Compiler

Compiled 39 to 31 computations (20.5% saved)

regimes7.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 1/2 x)
(tan.f64 (/.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
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 32 to 24 computations (25% 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
53.7%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify41.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
11018
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)

soundness41.0ms (0.7%)

Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
Stop Event
1×saturated
Compiler

Compiled 12 to 9 computations (25% saved)

end34.0ms (0.6%)

Compiler

Compiled 42 to 32 computations (23.8% saved)

Profiling

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