Kahan's exp quotient

Time bar (total: 3.2s)

analyze1.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample1.2s (38%)

Results
563.0ms2127×body1024valid
294.0ms2929×body256valid
150.0ms2015×body256infinite
133.0ms992×body512valid
52.0ms193×body2048valid
Bogosity

preprocess61.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1290×div-sub
1216×fma-neg
1162×fma-def
906×cancel-sign-sub-inv
870×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01241
12941
24741
37941
418541
554341
6163541
7579741
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x))
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 x))
Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Compiler

Compiled 5 to 3 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (expm1.f64 x) x)
▶100.0%
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 10 to 6 computations (40% saved)

localize36.0ms (1.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 9 to 4 computations (55.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 (expm1.f64 x) x)
0.0ms
x
@inf
(/.f64 (expm1.f64 x) x)
0.0ms
x
@0
(/.f64 (expm1.f64 x) x)

rewrite55.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
1246×pow1
1146×add-exp-log
1146×log1p-expm1-u
1144×expm1-log1p-u
1120×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
112011
2153711
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
Outputs
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

simplify53.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1756×fma-def
772×log-prod
580×div-sub
574×log-div
402×associate-*r/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
096551
1227547
2789539
34125527
Stop Event
1×node limit
Counts
43 → 47
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 x (*.f64 x 1/6))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 x (*.f64 x 1/6)))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (expm1.f64 x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval8.0ms (0.3%)

Compiler

Compiled 436 to 218 computations (50% saved)

prune10.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New42547
Fresh000
Picked011
Done000
Total42648
Accuracy
100.0%
Counts
48 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
✓100.0%
(/.f64 (expm1.f64 x) x)
▶77.2%
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
▶51.2%
(+.f64 1 (*.f64 1/2 x))
▶99.9%
(*.f64 (/.f64 1 x) (expm1.f64 x))
50.8%
1
▶100.0%
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
✓100.0%
(/.f64 (expm1.f64 x) x)
▶77.2%
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
▶51.2%
(+.f64 1 (*.f64 1/2 x))
▶99.9%
(*.f64 (/.f64 1 x) (expm1.f64 x))
50.8%
1
Compiler

Compiled 72 to 54 computations (25% saved)

localize87.0ms (2.7%)

Localize:

Found 6 expressions with local error:

NewAccuracyProgram
✓100.0%
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
✓100.0%
(/.f64 x (expm1.f64 x))
✓100.0%
(+.f64 1 (/.f64 (expm1.f64 x) x))
100.0%
(/.f64 (expm1.f64 x) x)
✓77.2%
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
✓99.9%
(*.f64 (/.f64 1 x) (expm1.f64 x))
Compiler

Compiled 62 to 29 computations (53.2% saved)

series3.0ms (0.1%)

Counts
5 → 60
Calls

15 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0ms
x
@inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0ms
x
@-inf
(/.f64 x (expm1.f64 x))
0.0ms
x
@inf
(/.f64 x (expm1.f64 x))
0.0ms
x
@inf
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)

rewrite118.0ms (3.7%)

Algorithm
1×batch-egg-rewrite
Rules
1738×prod-diff
1154×fma-def
1086×log-prod
402×expm1-udef
402×log1p-udef
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01461
130661
2361161
Stop Event
1×node limit
Counts
5 → 448
Calls
Call 1
Inputs
(*.f64 (/.f64 1 x) (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(+.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 x (expm1.f64 x))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
(+.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1))
(+.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1))
(+.f64 (/.f64 (expm1.f64 x) x) 0)
(+.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)
(+.f64 -1 (+.f64 1 (/.f64 (expm1.f64 x) x)))
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
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(+.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(-.f64 (/.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(-.f64 (/.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(*.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(*.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)))
(*.f64 (*.f64 (expm1.f64 x) (pow.f64 x -1/2)) (pow.f64 x -1/2))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))))
(/.f64 1 (/.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x))))))
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x))))) (neg.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1)) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1))) (-.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1)))
(/.f64 (*.f64 (expm1.f64 x) -1) (neg.f64 x))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 1))
(hypot.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (*.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(hypot.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (sqrt.f64 (*.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(fma.f64 1 (/.f64 (expm1.f64 x) x) 0)
(fma.f64 1 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)
(fma.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(fma.f64 (/.f64 1 x) (expm1.f64 x) 0)
(fma.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1) 0)
(fma.f64 (expm1.f64 x) (/.f64 1 x) 0)
(fma.f64 (/.f64 (expm1.f64 x) x) 1 0)
(fma.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1 -1)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 x)) 0)
(fma.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 0)
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(fma.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)) 0)
(fma.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (*.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) -1)
(fma.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(fma.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)) 0)
(fma.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (/.f64 1 (fma.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)) -1)
(fma.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))) 0)
(fma.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (-.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)) 0)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1))) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(fma.f64 (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(fma.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)) 0)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x) 0)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 0)
(fma.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)) 0)
(fma.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) 0)
(fma.f64 (+.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) (-.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) 1)
(fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)) 0)
(fma.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)) 0)
(fma.f64 (*.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) 0)
(fma.f64 (*.f64 (expm1.f64 x) (pow.f64 x -1/2)) (pow.f64 x -1/2) 0)

simplify145.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
1018×fma-neg
806×div-sub
528×log-prod
476×exp-prod
442×cube-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045611770
1101911300
2376811298
Stop Event
1×node limit
Counts
508 → 318
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 2 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
1
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
1
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
1
(+.f64 1 (*.f64 -1/2 x))
(+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))
(+.f64 1 (+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2)))))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(+.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1))
(+.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1))
(+.f64 (/.f64 (expm1.f64 x) x) 0)
(+.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)
(+.f64 -1 (+.f64 1 (/.f64 (expm1.f64 x) x)))
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
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(+.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(-.f64 (/.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(-.f64 (/.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(*.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(*.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)))
(*.f64 (*.f64 (expm1.f64 x) (pow.f64 x -1/2)) (pow.f64 x -1/2))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))))
(/.f64 1 (/.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x))))))
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x))))) (neg.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1)) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1))) (-.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1)))
(/.f64 (*.f64 (expm1.f64 x) -1) (neg.f64 x))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 1))
(hypot.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (*.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(hypot.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (sqrt.f64 (*.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(fma.f64 1 (/.f64 (expm1.f64 x) x) 0)
(fma.f64 1 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)
(fma.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(fma.f64 (/.f64 1 x) (expm1.f64 x) 0)
(fma.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1) 0)
(fma.f64 (expm1.f64 x) (/.f64 1 x) 0)
(fma.f64 (/.f64 (expm1.f64 x) x) 1 0)
(fma.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1 -1)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 x)) 0)
(fma.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 0)
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(fma.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)) 0)
(fma.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (*.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) -1)
(fma.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(fma.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)) 0)
(fma.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (/.f64 1 (fma.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)) -1)
(fma.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))) 0)
(fma.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (-.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)) 0)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1))) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(fma.f64 (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(fma.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)) 0)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x) 0)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 0)
(fma.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)) 0)
(fma.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) 0)
(fma.f64 (+.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) (-.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) 1)
(fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)) 0)
(fma.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)) 0)
(fma.f64 (*.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) 0)
(fma.f64 (*.f64 (expm1.f64 x) (pow.f64 x -1/2)) (pow.f64 x -1/2) 0)
Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x))))
(+.f64 (fma.f64 1/2 x 1) (*.f64 x (*.f64 x 1/6)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (*.f64 x 1/6))) (fma.f64 1/2 x 1))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x))))
(+.f64 (fma.f64 1/2 x 1) (*.f64 x (*.f64 x 1/6)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (*.f64 x 1/6))) (fma.f64 1/2 x 1))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 2 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 2 (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 2 (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x))))
(+.f64 (*.f64 x (*.f64 x 1/6)) (fma.f64 1/2 x 2))
(+.f64 2 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 2 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/6 (*.f64 x x))) (fma.f64 1/2 x 2))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (*.f64 x 1/6))) (fma.f64 1/2 x 2))
1
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
1
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) x)) (/.f64 1 x))
(+.f64 1 (/.f64 (expm1.f64 x) x))
1
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(+.f64 1 (*.f64 x -1/2))
(fma.f64 x -1/2 1)
(+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))
(+.f64 1 (fma.f64 -1/2 x (*.f64 (*.f64 x x) 1/12)))
(+.f64 1 (fma.f64 x -1/2 (*.f64 x (*.f64 x 1/12))))
(+.f64 1 (fma.f64 (*.f64 x x) 1/12 (*.f64 x -1/2)))
(+.f64 1 (+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 4) (*.f64 (*.f64 x x) 1/12))))
(+.f64 1 (fma.f64 x -1/2 (fma.f64 (*.f64 x x) 1/12 (*.f64 -1/720 (pow.f64 x 4)))))
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(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
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(+.f64 1 (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x))))
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(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (*.f64 x 1/6))) (fma.f64 1/2 x 1))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(+.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1))
(/.f64 (expm1.f64 x) x)
(+.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1))
(/.f64 (expm1.f64 x) x)
(+.f64 (/.f64 (expm1.f64 x) x) 0)
(/.f64 (expm1.f64 x) x)
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(/.f64 (expm1.f64 x) x)
(+.f64 -1 (+.f64 1 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
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(/.f64 (expm1.f64 x) x)
(+.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)
(/.f64 (expm1.f64 x) x)
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(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
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(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))))
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(/.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (+.f64 (/.f64 (expm1.f64 x) x) (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x))))))
(*.f64 (/.f64 1 (+.f64 2 (/.f64 (expm1.f64 x) x))) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (/.f64 (expm1.f64 x) x)))
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 2 (/.f64 (expm1.f64 x) x)))) (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (+.f64 (/.f64 (expm1.f64 x) x) (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2))))
(/.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1))))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 2 (/.f64 (expm1.f64 x) x)))) (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (+.f64 (/.f64 (expm1.f64 x) x) (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 (/.f64 (expm1.f64 x) x) 2))
(*.f64 (/.f64 1 (+.f64 2 (/.f64 (expm1.f64 x) x))) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (/.f64 (expm1.f64 x) x)))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))
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(*.f64 (/.f64 1 (+.f64 2 (/.f64 (expm1.f64 x) x))) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
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(fma.f64 (/.f64 1 x) (expm1.f64 x) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (expm1.f64 x) (/.f64 1 x) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 (expm1.f64 x) x) 1 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1 -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 x)) 0)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 (*.f64 1 (expm1.f64 x)) (cbrt.f64 x)) 0)
(*.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (expm1.f64 x) (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 x)))
(fma.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1) -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (*.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) -1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (/.f64 1 (fma.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)) -1)
(+.f64 (/.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (fma.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)) -1)
(+.f64 -1 (/.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (fma.f64 (/.f64 (expm1.f64 x) x) (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)))
(fma.f64 (expm1.f64 (*.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))) 0)
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 2 (/.f64 (expm1.f64 x) x)))) (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (+.f64 (/.f64 (expm1.f64 x) x) (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2))))
(fma.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (-.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(+.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (-.f64 1 (/.f64 (expm1.f64 x) x))) -1)
(+.f64 -1 (/.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (-.f64 1 (/.f64 (expm1.f64 x) x))))
(fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)) 0)
(*.f64 (/.f64 1 (+.f64 2 (/.f64 (expm1.f64 x) x))) (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 2 (/.f64 (expm1.f64 x) x)))
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1))) (cbrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) (sqrt.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1)) 1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(/.f64 1 (*.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x)))))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(fma.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)))
(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) 0)
(fma.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x)))) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) 0)
(*.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x)))) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))))
(*.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (expm1.f64 x) x)))) (+.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)))))
(fma.f64 (+.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) (-.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1) 1)
(/.f64 (expm1.f64 x) x)
(fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)) 0)
(/.f64 (expm1.f64 x) x)
(fma.f64 (*.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) 0)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 (*.f64 1 (expm1.f64 x)) (cbrt.f64 x)) 0)
(*.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (expm1.f64 x) (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 x)))
(fma.f64 (*.f64 (expm1.f64 x) (pow.f64 x -1/2)) (pow.f64 x -1/2) 0)
(/.f64 (expm1.f64 x) x)

eval86.0ms (2.7%)

Compiler

Compiled 5063 to 2623 computations (48.2% saved)

prune47.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3632365
Fresh011
Picked314
Done011
Total3665371
Accuracy
100.0%
Counts
371 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
▶100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
▶51.2%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
✓51.2%
(+.f64 1 (*.f64 1/2 x))
50.8%
1
✓100.0%
(/.f64 (expm1.f64 x) x)
▶100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
▶51.2%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
✓51.2%
(+.f64 1 (*.f64 1/2 x))
50.8%
1
Compiler

Compiled 56 to 44 computations (21.4% saved)

localize45.0ms (1.4%)

Localize:

Found 3 expressions with local error:

NewAccuracyProgram
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
100.0%
(/.f64 x (expm1.f64 x))
✓100.0%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
Compiler

Compiled 35 to 22 computations (37.1% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
0.0ms
x
@inf
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
0.0ms
x
@-inf
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0ms
x
@-inf
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
0.0ms
x
@0
(/.f64 1 (/.f64 x (expm1.f64 x)))

rewrite75.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
1232×log-prod
750×pow-prod-down
610×fma-def
590×pow-prod-up
588×pow-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01330
128820
2374620
Stop Event
1×node limit
Counts
2 → 117
Calls
Call 1
Inputs
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
(/.f64 1 (/.f64 x (expm1.f64 x)))
Outputs
(+.f64 (*.f64 1/2 x) 1)
(+.f64 2 (fma.f64 1/2 x -1))
(+.f64 (fma.f64 1/2 x 2) -1)
(+.f64 1 (*.f64 1/2 x))
(+.f64 0 (fma.f64 1/2 x 1))
(+.f64 -1 (fma.f64 1/2 x 2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1))) (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 x 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 x 1)))))
(*.f64 1 (fma.f64 1/2 x 1))
(*.f64 (fma.f64 1/2 x 1) 1)
(*.f64 (cbrt.f64 (fma.f64 1/2 x 1)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)))
(*.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)))
(*.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3))))
(*.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1) (/.f64 1 (fma.f64 1/2 x 3)))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1) (-.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)))
(/.f64 1 (/.f64 (fma.f64 1/2 x 3) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (-.f64 1 (*.f64 (fma.f64 1/2 x 2) -1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1) (fma.f64 1/2 x 3))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)) (neg.f64 (fma.f64 1/2 x 3)))
(/.f64 (fma.f64 1/8 (pow.f64 x 3) 1) (fma.f64 1/4 (*.f64 x x) (-.f64 1 (*.f64 1/2 x))))
(/.f64 (fma.f64 1/4 (*.f64 x x) -1) (fma.f64 1/2 x -1))
(pow.f64 (fma.f64 1/2 x 1) 1)
(pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 3)
(pow.f64 (pow.f64 (fma.f64 1/2 x 1) 2) 1/2)
(pow.f64 (pow.f64 (fma.f64 1/2 x 1) 3) 1/3)
(pow.f64 (sqrt.f64 (fma.f64 1/2 x 1)) 2)
(pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)) -1)
(pow.f64 (/.f64 (fma.f64 1/2 x 3) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)) -1)
(sqrt.f64 (pow.f64 (fma.f64 1/2 x 1) 2))
(log.f64 (exp.f64 (fma.f64 1/2 x 1)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 x 1))))
(cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/2 x 1)))
(expm1.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) 1))
(exp.f64 (log1p.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) 1))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) 1) 1))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (*.f64 1/2 x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (*.f64 1/2 x))) 1/3))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (*.f64 1/2 x))) 2))
(log1p.f64 (expm1.f64 (fma.f64 1/2 x 1)))
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(fma.f64 (*.f64 1/2 x) 1 1)
(fma.f64 (fma.f64 1/2 x 2) 1 -1)
(fma.f64 1 (*.f64 1/2 x) 1)
(fma.f64 1 (fma.f64 1/2 x 2) -1)
(fma.f64 (cbrt.f64 (*.f64 1/2 x)) (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) 1)
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) 1)
(fma.f64 (cbrt.f64 (fma.f64 1/2 x 2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (cbrt.f64 (fma.f64 1/2 x 2)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (*.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) 1)
(fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) 1)
(fma.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (sqrt.f64 (fma.f64 1/2 x 2)) -1)
(fma.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (*.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1) -1)
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) 1)
(fma.f64 (fma.f64 1/8 (pow.f64 x 3) 8) (/.f64 1 (fma.f64 1/4 (*.f64 x x) (-.f64 4 x))) -1)
(fma.f64 (fma.f64 1/4 (*.f64 x x) -4) (/.f64 1 (fma.f64 1/2 x -2)) -1)
(fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1)
(fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) 1)
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (/.f64 1 (/.f64 1 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))
(*.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (cbrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) -2))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) -2) -1/2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -2)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (neg.f64 (/.f64 (neg.f64 x) (expm1.f64 x))) -1)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) 1) -1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

simplify87.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
1238×fma-def
772×distribute-lft-in
752×distribute-rgt-in
506×fma-neg
506×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02952447
16492341
217482271
377202271
Stop Event
1×node limit
Counts
141 → 148
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(+.f64 (*.f64 1/2 x) 1)
(+.f64 2 (fma.f64 1/2 x -1))
(+.f64 (fma.f64 1/2 x 2) -1)
(+.f64 1 (*.f64 1/2 x))
(+.f64 0 (fma.f64 1/2 x 1))
(+.f64 -1 (fma.f64 1/2 x 2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1))) (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 x 1)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 x 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 x 1)))))
(*.f64 1 (fma.f64 1/2 x 1))
(*.f64 (fma.f64 1/2 x 1) 1)
(*.f64 (cbrt.f64 (fma.f64 1/2 x 1)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)))
(*.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)))
(*.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3))))
(*.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1) (/.f64 1 (fma.f64 1/2 x 3)))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1) (-.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)))
(/.f64 1 (/.f64 (fma.f64 1/2 x 3) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (-.f64 1 (*.f64 (fma.f64 1/2 x 2) -1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1) (fma.f64 1/2 x 3))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)) (neg.f64 (fma.f64 1/2 x 3)))
(/.f64 (fma.f64 1/8 (pow.f64 x 3) 1) (fma.f64 1/4 (*.f64 x x) (-.f64 1 (*.f64 1/2 x))))
(/.f64 (fma.f64 1/4 (*.f64 x x) -1) (fma.f64 1/2 x -1))
(pow.f64 (fma.f64 1/2 x 1) 1)
(pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 3)
(pow.f64 (pow.f64 (fma.f64 1/2 x 1) 2) 1/2)
(pow.f64 (pow.f64 (fma.f64 1/2 x 1) 3) 1/3)
(pow.f64 (sqrt.f64 (fma.f64 1/2 x 1)) 2)
(pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) (fma.f64 1/2 x 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1)) -1)
(pow.f64 (/.f64 (fma.f64 1/2 x 3) (+.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1)) -1)
(sqrt.f64 (pow.f64 (fma.f64 1/2 x 1) 2))
(log.f64 (exp.f64 (fma.f64 1/2 x 1)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 x 1))))
(cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/2 x 1)))
(expm1.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) 1))
(exp.f64 (log1p.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) 1))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) 1) 1))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (*.f64 1/2 x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (*.f64 1/2 x))) 1/3))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (*.f64 1/2 x))) 2))
(log1p.f64 (expm1.f64 (fma.f64 1/2 x 1)))
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(fma.f64 (*.f64 1/2 x) 1 1)
(fma.f64 (fma.f64 1/2 x 2) 1 -1)
(fma.f64 1 (*.f64 1/2 x) 1)
(fma.f64 1 (fma.f64 1/2 x 2) -1)
(fma.f64 (cbrt.f64 (*.f64 1/2 x)) (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) 1)
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) 1)
(fma.f64 (cbrt.f64 (fma.f64 1/2 x 2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (cbrt.f64 (fma.f64 1/2 x 2)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (*.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) 1)
(fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) 1)
(fma.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (sqrt.f64 (fma.f64 1/2 x 2)) -1)
(fma.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (*.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 1) -1)
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) 1)
(fma.f64 (fma.f64 1/8 (pow.f64 x 3) 8) (/.f64 1 (fma.f64 1/4 (*.f64 x x) (-.f64 4 x))) -1)
(fma.f64 (fma.f64 1/4 (*.f64 x x) -4) (/.f64 1 (fma.f64 1/2 x -2)) -1)
(fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1)
(fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) 1)
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (/.f64 1 (/.f64 1 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 2)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))
(*.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (cbrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) -2))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) -2) -1/2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -2)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (neg.f64 (/.f64 (neg.f64 x) (expm1.f64 x))) -1)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) 1) -1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 (*.f64 x (*.f64 x 1/6)) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 x 3)) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (*.f64 x 1/6))) (fma.f64 1/2 x 1))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 2 (fma.f64 1/2 x -1))
(fma.f64 1/2 x 1)
(+.f64 (fma.f64 1/2 x 2) -1)
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 0 (fma.f64 1/2 x 1))
(fma.f64 1/2 x 1)
(+.f64 -1 (fma.f64 1/2 x 2))
(fma.f64 1/2 x 1)
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval49.0ms (1.6%)

Compiler

Compiled 2226 to 1382 computations (37.9% saved)

prune29.0ms (0.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New2002202
Fresh011
Picked022
Done022
Total2007207
Accuracy
100.0%
Counts
207 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
▶54.4%
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
✓51.2%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
✓51.2%
(+.f64 1 (*.f64 1/2 x))
▶3.9%
(*.f64 1/2 x)
50.8%
1
✓100.0%
(/.f64 (expm1.f64 x) x)
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
▶54.4%
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
✓51.2%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
✓51.2%
(+.f64 1 (*.f64 1/2 x))
▶3.9%
(*.f64 1/2 x)
50.8%
1
Compiler

Compiled 80 to 64 computations (20% saved)

localize34.0ms (1.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
Compiler

Compiled 25 to 19 computations (24% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
0.0ms
x
@0
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
0.0ms
x
@-inf
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))

rewrite53.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
1602×pow1
1486×add-exp-log
1486×log1p-expm1-u
1486×expm1-log1p-u
1458×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0819
116915
2208415
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
Outputs
(-.f64 (+.f64 1 (/.f64 1 (fma.f64 x -1/2 1))) 1)
(*.f64 1 (/.f64 1 (fma.f64 x -1/2 1)))
(*.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))))
(*.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) (pow.f64 (fma.f64 x -1/2 1) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x -1/2 1))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) 2)) -1) (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) -1))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 (*.f64 x -1/2) 3))) (+.f64 1 (+.f64 (pow.f64 (*.f64 x -1/2) 2) (*.f64 1/2 x))))
(*.f64 (/.f64 1 (-.f64 1 (pow.f64 (*.f64 x -1/2) 2))) (+.f64 1 (*.f64 1/2 x)))
(pow.f64 (fma.f64 x -1/2 1) -1)
(pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) 3)
(pow.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3) 1/3)
(pow.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) 2)
(sqrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2))
(log.f64 (exp.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x -1/2 1))))

simplify62.0ms (2%)

Algorithm
1×egg-herbie
Rules
710×associate-*r*
658×associate-*l*
594×fma-def
570×associate-/l/
508×fma-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01001068
1277908
2817794
33982794
Stop Event
1×node limit
Counts
34 → 62
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 3)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 16 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 x))))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 16 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 x))))))
(-.f64 (+.f64 1 (/.f64 1 (fma.f64 x -1/2 1))) 1)
(*.f64 1 (/.f64 1 (fma.f64 x -1/2 1)))
(*.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))))
(*.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) (pow.f64 (fma.f64 x -1/2 1) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x -1/2 1))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) 2)) -1) (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) -1))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 (*.f64 x -1/2) 3))) (+.f64 1 (+.f64 (pow.f64 (*.f64 x -1/2) 2) (*.f64 1/2 x))))
(*.f64 (/.f64 1 (-.f64 1 (pow.f64 (*.f64 x -1/2) 2))) (+.f64 1 (*.f64 1/2 x)))
(pow.f64 (fma.f64 x -1/2 1) -1)
(pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) 3)
(pow.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3) 1/3)
(pow.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) 2)
(sqrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2))
(log.f64 (exp.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x -1/2 1))))
Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/4 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 1/4 (*.f64 x x))))
(fma.f64 1/2 x (fma.f64 1/4 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 3)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/8 (pow.f64 x 3) (fma.f64 1/4 (*.f64 x x) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/8 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/4 (*.f64 x x)))))
(fma.f64 1/8 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 1/4 (*.f64 x x) 1)))
(fma.f64 1/8 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1)))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(neg.f64 (+.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x))))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3)))))
(-.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3))))
(+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -2 x) (/.f64 -8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3)))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 16 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 x))))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 16 (pow.f64 x 4)))))
(+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 -8 (pow.f64 x 3))) (/.f64 16 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 3))) (-.f64 (/.f64 -2 x) (/.f64 16 (pow.f64 x 4))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(neg.f64 (+.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x))))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3)))))
(-.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3))))
(+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -2 x) (/.f64 -8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3)))
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 16 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 x))))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 16 (pow.f64 x 4)))))
(+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 -8 (pow.f64 x 3))) (/.f64 16 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 3))) (-.f64 (/.f64 -2 x) (/.f64 16 (pow.f64 x 4))))
(-.f64 (+.f64 1 (/.f64 1 (fma.f64 x -1/2 1))) 1)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 1 (/.f64 1 (fma.f64 x -1/2 1)))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)))
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (cbrt.f64 (fma.f64 x -1/2 1)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)))
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (cbrt.f64 (fma.f64 x -1/2 1)))
(*.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) (pow.f64 (fma.f64 x -1/2 1) -1/2))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x -1/2 1))))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) 2)) -1) (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) -1))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) 2))))
(/.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) 2)))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -1))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 (*.f64 x -1/2) 3))) (+.f64 1 (+.f64 (pow.f64 (*.f64 x -1/2) 2) (*.f64 1/2 x))))
(*.f64 (/.f64 1 (+.f64 1 (*.f64 (pow.f64 x 3) -1/8))) (+.f64 1 (+.f64 (*.f64 1/2 x) (pow.f64 (*.f64 x -1/2) 2))))
(/.f64 (+.f64 1 (fma.f64 1/2 x (*.f64 1/4 (*.f64 x x)))) (fma.f64 (pow.f64 x 3) -1/8 1))
(/.f64 (fma.f64 1/2 x (fma.f64 1/4 (*.f64 x x) 1)) (fma.f64 (pow.f64 x 3) -1/8 1))
(/.f64 (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1)) (fma.f64 (pow.f64 x 3) -1/8 1))
(*.f64 (/.f64 1 (-.f64 1 (pow.f64 (*.f64 x -1/2) 2))) (+.f64 1 (*.f64 1/2 x)))
(*.f64 (+.f64 1 (*.f64 1/2 x)) (/.f64 1 (-.f64 1 (pow.f64 (*.f64 x -1/2) 2))))
(/.f64 (fma.f64 1/2 x 1) (-.f64 1 (*.f64 1/4 (*.f64 x x))))
(/.f64 (fma.f64 1/2 x 1) (+.f64 1 (*.f64 x (*.f64 x -1/4))))
(pow.f64 (fma.f64 x -1/2 1) -1)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x -1/2 1))) 3)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3) 1/3)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (pow.f64 (fma.f64 x -1/2 1) -1/2) 2)
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(sqrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(log.f64 (exp.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x -1/2 1)) 3))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x -1/2 1))))
(+.f64 1 (-.f64 (/.f64 1 (fma.f64 x -1/2 1)) 1))
(+.f64 (/.f64 1 (fma.f64 x -1/2 1)) 0)
(/.f64 1 (fma.f64 x -1/2 1))

eval61.0ms (1.9%)

Compiler

Compiled 780 to 613 computations (21.4% saved)

prune13.0ms (0.4%)

Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New60262
Fresh011
Picked022
Done044
Total60969
Accuracy
100.0%
Counts
69 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
✓54.4%
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
6.6%
(/.f64 -2 x)
✓51.2%
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
5.4%
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
✓51.2%
(+.f64 1 (*.f64 1/2 x))
✓3.9%
(*.f64 1/2 x)
50.8%
1
Compiler

Compiled 126 to 88 computations (30.2% saved)

regimes13.0ms (0.4%)

Counts
13 → 1
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(/.f64 -2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
Calls

2 calls:

7.0ms
x
4.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 81 to 52 computations (35.8% saved)

regimes56.0ms (1.8%)

Counts
9 → 1
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(/.f64 -2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
Outputs
(/.f64 (expm1.f64 x) x)
Calls

1 calls:

54.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
Compiler

Compiled 48 to 34 computations (29.2% saved)

regimes7.0ms (0.2%)

Counts
7 → 1
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(/.f64 -2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
Outputs
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
Calls

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
54.4%1x
Compiler

Compiled 38 to 29 computations (23.7% saved)

regimes22.0ms (0.7%)

Counts
5 → 2
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(/.f64 -2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 2) 1)
Outputs
(/.f64 -2 x)
(+.f64 1 (*.f64 1/2 x))
Calls

1 calls:

21.0ms
x
Results
AccuracySegmentsBranch
55.5%2x
Compiler

Compiled 22 to 17 computations (22.7% saved)

regimes7.0ms (0.2%)

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

1 calls:

6.0ms
x
Results
AccuracySegmentsBranch
54.2%2x
Compiler

Compiled 10 to 7 computations (30% saved)

regimes26.0ms (0.8%)

Accuracy

Total -30.4b remaining (-96.6%)

Threshold costs -30.4b (-96.6%)

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

1 calls:

26.0ms
x
Results
AccuracySegmentsBranch
50.8%1x
Compiler

Compiled 7 to 5 computations (28.6% saved)

bsearch12.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
-125.41748141882452
-1.0405022567287598
Results
11.0ms112×body256valid
Compiler

Compiled 95 to 78 computations (17.9% saved)

bsearch13.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
-125.41748141882452
-1.0405022567287598
Results
11.0ms112×body256valid
Compiler

Compiled 67 to 57 computations (14.9% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
4×*-commutative
2×1-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02694
13294
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 1 (*.f64 1/2 x)))
(if (<=.f64 x -2) (/.f64 -2 x) 1)
1
Outputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 1 (*.f64 1/2 x)))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 1 (*.f64 x 1/2)))
(if (<=.f64 x -2) (/.f64 -2 x) 1)
1
Compiler

Compiled 44 to 34 computations (22.7% saved)

soundness521.0ms (16.4%)

Rules
1738×prod-diff
1290×div-sub
1246×pow1
1216×fma-neg
1162×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01241
12941
24741
37941
418541
554341
6163541
7579741
0611
112011
2153711
01461
130661
2361161
045611770
1101911300
2376811298
Stop Event
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 56 to 37 computations (33.9% saved)

end0.0ms (0%)

preprocess59.0ms (1.9%)

Compiler

Compiled 138 to 96 computations (30.4% saved)

Profiling

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