Kahan's exp quotient

Time bar (total: 2.2s)

analyze1.0ms (0.1%)

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)

sample1.3s (56.7%)

Results
525.0ms2095×body1024valid
335.0ms2926×body256valid
192.0ms2027×body256infinite
135.0ms1012×body512valid
52.0ms196×body2048valid
Bogosity

preprocess57.0ms (2.6%)

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
01230
12930
24730
37930
418530
554330
6163530
7579730
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.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 (neg.f64 x)) 1) (neg.f64 x))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify17.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
336×fma-def
68×distribute-rgt-in
52×distribute-lft-in
40×sub-neg
40×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11711
22011
32411
43311
54311
66211
710311
814711
922511
1034711
1153111
1260311
1363911
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval0.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% 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%
(/.f64 (expm1.f64 x) x)
▶100.0%
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 10 to 6 computations (40% saved)

localize22.0ms (1%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiled 9 to 4 computations (55.6% saved)

series1.0ms (0.1%)

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)

rewrite50.0ms (2.3%)

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)))

simplify48.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
1732×fma-def
772×log-prod
592×div-sub
574×log-div
400×associate-*r/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
097543
1230539
2789539
34114527
Stop Event
1×node limit
Counts
43 → 46
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.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 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(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 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 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 (0.4%)

Compiler

Compiled 424 to 210 computations (50.5% saved)

prune13.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New43346
Fresh000
Picked011
Done000
Total43447
Accurracy
100.0%
Counts
47 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
▶54.0%
(+.f64 (*.f64 1/2 x) 1)
▶99.5%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
✓100.0%
(/.f64 (expm1.f64 x) x)
▶54.0%
(+.f64 (*.f64 1/2 x) 1)
▶99.5%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
Compiler

Compiled 60 to 44 computations (26.7% saved)

localize85.0ms (3.9%)

Local Accuracy

Found 4 expressions with local accuracy:

NewAccuracyProgram
✓99.5%
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
✓99.5%
(cbrt.f64 (expm1.f64 x))
✓99.2%
(pow.f64 (cbrt.f64 x) 2)
✓99.1%
(cbrt.f64 x)
Compiler

Compiled 66 to 31 computations (53% saved)

series11.0ms (0.5%)

Counts
4 → 16
Calls

12 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
(cbrt.f64 (expm1.f64 x))
2.0ms
x
@inf
(cbrt.f64 (expm1.f64 x))
1.0ms
x
@0
(cbrt.f64 x)
1.0ms
x
@-inf
(cbrt.f64 x)
0.0ms
x
@-inf
(pow.f64 (cbrt.f64 x) 2)

rewrite64.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
1482×pow1
1362×add-exp-log
1362×log1p-expm1-u
1360×expm1-log1p-u
1326×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01040
119340
2204240
Stop Event
1×node limit
Counts
4 → 72
Calls
Call 1
Inputs
(cbrt.f64 x)
(pow.f64 (cbrt.f64 x) 2)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
Outputs
(-.f64 (+.f64 1 (cbrt.f64 x)) 1)
(*.f64 (cbrt.f64 x) 1)
(*.f64 1 (cbrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x)))
(*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(*.f64 (pow.f64 x 1/6) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 x))
(*.f64 (pow.f64 (sqrt.f64 x) 1/3) (pow.f64 (sqrt.f64 x) 1/3))
(pow.f64 x 1/3)
(pow.f64 (cbrt.f64 x) 1)
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
(pow.f64 (pow.f64 x 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 x) 2))
(fabs.f64 (cbrt.f64 x))
(log.f64 (exp.f64 (cbrt.f64 x)))
(expm1.f64 (log1p.f64 (cbrt.f64 x)))
(exp.f64 (log.f64 (cbrt.f64 x)))
(log1p.f64 (expm1.f64 (cbrt.f64 x)))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(*.f64 (sqrt.f64 x) (pow.f64 x 1/6))
(*.f64 (pow.f64 x 1/6) (*.f64 (pow.f64 x 1/6) (cbrt.f64 x)))
(*.f64 (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(cbrt.f64 (*.f64 x x))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 x))))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(-.f64 (+.f64 1 (cbrt.f64 (expm1.f64 x))) 1)
(*.f64 (cbrt.f64 (expm1.f64 x)) 1)
(*.f64 1 (cbrt.f64 (expm1.f64 x)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3))
(pow.f64 (expm1.f64 x) 1/3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 1)
(pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(fabs.f64 (cbrt.f64 (expm1.f64 x)))
(log.f64 (exp.f64 (cbrt.f64 (expm1.f64 x))))
(expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 x))))
(exp.f64 (log.f64 (cbrt.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (cbrt.f64 (expm1.f64 x))))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) 1)
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (*.f64 (pow.f64 (expm1.f64 x) 1/6) (cbrt.f64 (expm1.f64 x))))
(*.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (expm1.f64 x)))))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))

simplify60.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
1576×fma-def
940×unswap-sqr
860×exp-prod
542×distribute-rgt-in
534×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01401626
12431368
28781112
335391096
Stop Event
1×node limit
Counts
88 → 93
Calls
Call 1
Inputs
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(-.f64 (+.f64 1 (cbrt.f64 x)) 1)
(*.f64 (cbrt.f64 x) 1)
(*.f64 1 (cbrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x)))
(*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(*.f64 (pow.f64 x 1/6) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 x))
(*.f64 (pow.f64 (sqrt.f64 x) 1/3) (pow.f64 (sqrt.f64 x) 1/3))
(pow.f64 x 1/3)
(pow.f64 (cbrt.f64 x) 1)
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
(pow.f64 (pow.f64 x 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 x) 2))
(fabs.f64 (cbrt.f64 x))
(log.f64 (exp.f64 (cbrt.f64 x)))
(expm1.f64 (log1p.f64 (cbrt.f64 x)))
(exp.f64 (log.f64 (cbrt.f64 x)))
(log1p.f64 (expm1.f64 (cbrt.f64 x)))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(*.f64 (sqrt.f64 x) (pow.f64 x 1/6))
(*.f64 (pow.f64 x 1/6) (*.f64 (pow.f64 x 1/6) (cbrt.f64 x)))
(*.f64 (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(cbrt.f64 (*.f64 x x))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 x))))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(-.f64 (+.f64 1 (cbrt.f64 (expm1.f64 x))) 1)
(*.f64 (cbrt.f64 (expm1.f64 x)) 1)
(*.f64 1 (cbrt.f64 (expm1.f64 x)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3))
(pow.f64 (expm1.f64 x) 1/3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 1)
(pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(fabs.f64 (cbrt.f64 (expm1.f64 x)))
(log.f64 (exp.f64 (cbrt.f64 (expm1.f64 x))))
(expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 x))))
(exp.f64 (log.f64 (cbrt.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (cbrt.f64 (expm1.f64 x))))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) 1)
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (*.f64 (pow.f64 (expm1.f64 x) 1/6) (cbrt.f64 (expm1.f64 x))))
(*.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (expm1.f64 x)))))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
Outputs
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(-.f64 (+.f64 1 (cbrt.f64 x)) 1)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (cbrt.f64 x) 1)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 1 (cbrt.f64 x))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (pow.f64 x 1/6) (pow.f64 x 1/6))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x)))) (fabs.f64 (cbrt.f64 (cbrt.f64 x))))
(*.f64 (cbrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x)))))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 x))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(*.f64 (pow.f64 (sqrt.f64 x) 1/3) (pow.f64 (sqrt.f64 x) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(pow.f64 (pow.f64 (sqrt.f64 x) 1/6) 4)
(pow.f64 x 1/3)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(pow.f64 (cbrt.f64 x) 1)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(pow.f64 (pow.f64 x 1/6) 2)
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(sqrt.f64 (pow.f64 (cbrt.f64 x) 2))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(fabs.f64 (cbrt.f64 x))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(log.f64 (exp.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(expm1.f64 (log1p.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(exp.f64 (log.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(log1p.f64 (expm1.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (cbrt.f64 x) 1))
(+.f64 (cbrt.f64 x) 0)
(cbrt.f64 x)
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (sqrt.f64 x) (pow.f64 x 1/6))
(*.f64 (pow.f64 x 1/6) (sqrt.f64 x))
(*.f64 (pow.f64 x 1/6) (*.f64 (pow.f64 x 1/6) (cbrt.f64 x)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(cbrt.f64 (*.f64 x x))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 x))))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(-.f64 (+.f64 1 (cbrt.f64 (expm1.f64 x))) 1)
(cbrt.f64 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) 1)
(cbrt.f64 (expm1.f64 x))
(*.f64 1 (cbrt.f64 (expm1.f64 x)))
(cbrt.f64 (expm1.f64 x))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(cbrt.f64 (expm1.f64 x))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(cbrt.f64 (expm1.f64 x))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (expm1.f64 x) 1/6))
(cbrt.f64 (expm1.f64 x))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2)))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (expm1.f64 x)))
(cbrt.f64 (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 1/6) 4)
(pow.f64 (expm1.f64 x) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (cbrt.f64 (expm1.f64 x)) 1)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1/2)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) 1/6) 2)
(cbrt.f64 (expm1.f64 x))
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(cbrt.f64 (expm1.f64 x))
(fabs.f64 (cbrt.f64 (expm1.f64 x)))
(cbrt.f64 (expm1.f64 x))
(log.f64 (exp.f64 (cbrt.f64 (expm1.f64 x))))
(cbrt.f64 (expm1.f64 x))
(expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 x))))
(cbrt.f64 (expm1.f64 x))
(exp.f64 (log.f64 (cbrt.f64 (expm1.f64 x))))
(cbrt.f64 (expm1.f64 x))
(log1p.f64 (expm1.f64 (cbrt.f64 (expm1.f64 x))))
(cbrt.f64 (expm1.f64 x))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) 1)
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (expm1.f64 x)))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1)
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (expm1.f64 x))))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2))
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 1/6))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (*.f64 (pow.f64 (expm1.f64 x) 1/6) (cbrt.f64 (expm1.f64 x))))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (expm1.f64 x)))))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(+.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1)
(+.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 0)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)

eval31.0ms (1.4%)

Compiler

Compiled 1846 to 810 computations (56.1% saved)

prune41.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New92193
Fresh011
Picked112
Done011
Total93497
Accurracy
100.0%
Counts
97 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓54.0%
(+.f64 (*.f64 1/2 x) 1)
▶50.6%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
✓100.0%
(/.f64 (expm1.f64 x) x)
✓54.0%
(+.f64 (*.f64 1/2 x) 1)
▶50.6%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
Compiler

Compiled 60 to 42 computations (30% saved)

localize73.0ms (3.3%)

Local Accuracy

Found 4 expressions with local accuracy:

NewAccuracyProgram
✓99.7%
(cbrt.f64 (/.f64 (expm1.f64 x) x))
99.5%
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
99.5%
(cbrt.f64 (expm1.f64 x))
✓51.5%
(cbrt.f64 (*.f64 x x))
Compiler

Compiled 56 to 18 computations (67.9% saved)

series1.0ms (0.1%)

Counts
2 → 4
Calls

6 calls:

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

rewrite66.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
1642×pow1
1516×add-exp-log
1516×log1p-expm1-u
1514×expm1-log1p-u
1478×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
117526
2213226
Stop Event
1×node limit
Counts
2 → 44
Calls
Call 1
Inputs
(cbrt.f64 (*.f64 x x))
(cbrt.f64 (/.f64 (expm1.f64 x) x))
Outputs
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(*.f64 (pow.f64 1 1/3) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(pow.f64 x 2/3)
(pow.f64 (*.f64 x x) 1/3)
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) 3)
(pow.f64 (cbrt.f64 x) 2)
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(exp.f64 (log.f64 (pow.f64 (cbrt.f64 x) 2)))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(-.f64 (+.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 1)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(*.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 1 x) 1/3))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 (cbrt.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3) (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3))
(/.f64 1 (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 1 (/.f64 (cbrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(/.f64 (cbrt.f64 (neg.f64 (expm1.f64 x))) (cbrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) (neg.f64 (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(log.f64 (exp.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(exp.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))

simplify64.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
1462×fma-def
976×times-frac
702×exp-prod
650×log-prod
554×*-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01081212
12141004
2570818
32048788
45750788
Stop Event
1×node limit
Counts
48 → 66
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 1/36 (pow.f64 x 2))))
(+.f64 1 (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2)))))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(*.f64 (pow.f64 1 1/3) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(pow.f64 x 2/3)
(pow.f64 (*.f64 x x) 1/3)
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) 3)
(pow.f64 (cbrt.f64 x) 2)
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(exp.f64 (log.f64 (pow.f64 (cbrt.f64 x) 2)))
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(-.f64 (+.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 1)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(*.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 1 x) 1/3))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 (cbrt.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3) (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3))
(/.f64 1 (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 1 (/.f64 (cbrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(/.f64 (cbrt.f64 (neg.f64 (expm1.f64 x))) (cbrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) (neg.f64 (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(log.f64 (exp.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(exp.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
Outputs
1
(+.f64 1 (*.f64 1/6 x))
(fma.f64 1/6 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 1/36 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/6 x (*.f64 1/36 (*.f64 x x))))
(+.f64 1 (fma.f64 1/6 x (*.f64 x (*.f64 x 1/36))))
(fma.f64 1/6 x (fma.f64 1/36 (*.f64 x x) 1))
(fma.f64 x (fma.f64 x 1/36 1/6) 1)
(+.f64 1 (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 1/6 x (fma.f64 1/324 (pow.f64 x 3) (*.f64 1/36 (*.f64 x x)))))
(+.f64 1 (fma.f64 1/6 x (fma.f64 1/36 (*.f64 x x) (*.f64 1/324 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/6 x 1) (*.f64 (*.f64 x x) (+.f64 1/36 (*.f64 x 1/324))))
(fma.f64 1/6 x (fma.f64 x (*.f64 x (fma.f64 x 1/324 1/36)) 1))
(-.f64 (+.f64 1 (pow.f64 (cbrt.f64 x) 2)) 1)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 1 (pow.f64 (cbrt.f64 x) 2))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (pow.f64 1 1/3) (pow.f64 (cbrt.f64 x) 2))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(*.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 x (cbrt.f64 x))))
(pow.f64 x 2/3)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(pow.f64 (*.f64 x x) 1/3)
(cbrt.f64 (*.f64 x x))
(pow.f64 (pow.f64 (cbrt.f64 x) 2) 1)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) 3)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(pow.f64 (cbrt.f64 x) 2)
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(sqrt.f64 (*.f64 x (cbrt.f64 x)))
(log.f64 (exp.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(exp.f64 (log.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 x) 2)))
(+.f64 1 (-.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(+.f64 (pow.f64 (cbrt.f64 x) 2) 0)
(pow.f64 (cbrt.f64 x) 2)
(-.f64 (+.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 1 x) 1/3))
(*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 (cbrt.f64 x)))
(/.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) 1) (cbrt.f64 x))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3) (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/6) 4)
(/.f64 1 (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 1 (/.f64 (cbrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) 1) (cbrt.f64 x))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(/.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) 1) (cbrt.f64 x))
(/.f64 (cbrt.f64 (neg.f64 (expm1.f64 x))) (cbrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) (neg.f64 (cbrt.f64 x)))
(/.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) 1) (cbrt.f64 x))
(/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) x) 1/3)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 2)
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(log.f64 (exp.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(exp.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))
(log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(+.f64 1 (-.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1))
(+.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 0)
(cbrt.f64 (/.f64 (expm1.f64 x) x))

eval37.0ms (1.7%)

Compiler

Compiled 2224 to 862 computations (61.2% saved)

prune16.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done022
Total1124116
Accurracy
100.0%
Counts
116 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓54.0%
(+.f64 (*.f64 1/2 x) 1)
✓50.6%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
✓100.0%
(/.f64 (expm1.f64 x) x)
✓54.0%
(+.f64 (*.f64 1/2 x) 1)
✓50.6%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
Compiler

Compiled 60 to 42 computations (30% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Accurracy
100.0%
Counts
4 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓54.0%
(+.f64 (*.f64 1/2 x) 1)
✓50.6%
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
54.0%
1
Compiler

Compiled 79 to 48 computations (39.2% saved)

regimes9.0ms (0.4%)

Counts
6 → 1
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.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)))
Outputs
(/.f64 (expm1.f64 x) x)
Calls

2 calls:

4.0ms
x
3.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 58 to 33 computations (43.1% saved)

regimes4.0ms (0.2%)

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

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
54.0%1x
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
1
Outputs
1
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
54.0%1x
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
11425
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
(+.f64 (*.f64 1/2 x) 1)
1
Outputs
(/.f64 (expm1.f64 x) x)
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 x 1/2) 1)
1
Compiler

Compiled 13 to 10 computations (23.1% saved)

soundness63.0ms (2.8%)

Rules
336×fma-def
68×distribute-rgt-in
52×distribute-lft-in
40×sub-neg
40×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11711
22011
32411
43311
54311
66211
710311
814711
922511
1034711
1153111
1260311
1363911
Stop Event
1×saturated
Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess98.0ms (4.4%)

Compiler

Compiled 82 to 56 computations (31.7% saved)

Profiling

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