Kahan's exp quotient

Time bar (total: 3.8s)

analyze2.0ms (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)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
Operation ival-sub, time spent: 0.0ms, 0.0% of total-time
Operation ival-div, time spent: 0.0ms, 0.0% of total-time
Operation ival-exp, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.4s (38.1%)

Results
366.0ms2953×256valid
536.0ms2064×1024valid
181.0ms2056×256infinite
210.0ms1034×512valid
48.0ms148×2048valid
0.0ms1×512valid
Precisions
Click to see histograms. Total time spent on operations: 552.0ms
Operation ival-exp, time spent: 308.0ms, 56.0% of total-time
Operation ival-div, time spent: 119.0ms, 22.0% of total-time
Operation ival-sub, time spent: 104.0ms, 19.0% of total-time
Operation const, time spent: 22.0ms, 4.0% of total-time
Bogosity

preprocess203.0ms (5.4%)

Algorithm
1×egg-herbie
Rules
636×fma-define
382×fma-neg
222×times-frac
194×div-sub
128×distribute-rgt-in
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1440-0-(-.f64 (exp.f64 x) 1)
00-0-x
00-0-(exp.f64 x)
00-0-(/.f64 (-.f64 (exp.f64 x) 1) x)
00-0-1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01588
14380
28880
324080
463080
597280
6134280
7158680
8165780
Stop Event
1×saturated
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))
(neg.f64 (/.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))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x)))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(/.f64 (expm1.f64 (neg.f64 x)) x)
Compiler

Compiled 39 to 23 computations (41% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
Operation ival-exp, time spent: 20.0ms, 48.0% of total-time
Operation ival-sub, time spent: 12.0ms, 29.0% of total-time
Operation ival-div, time spent: 7.0ms, 17.0% of total-time
Operation const, time spent: 2.0ms, 5.0% of total-time

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)
Compiler

Compiled 5 to 3 computations (40% saved)

localize146.0ms (3.9%)

Localize:

Found 1 expressions with local error:

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

Compiled 9 to 4 computations (55.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 237.0ms
Operation composed, time spent: 117.0ms, 49.0% of total-time
Operation ival-exp, time spent: 112.0ms, 47.0% of total-time
Operation ival-div, time spent: 4.0ms, 2.0% of total-time
Operation ival-sub, time spent: 3.0ms, 1.0% of total-time
Operation const, time spent: 1.0ms, 0.0% of total-time

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite186.0ms (4.9%)

Algorithm
1×batch-egg-rewrite
Rules
628×unpow-prod-down
362×cbrt-prod
360×log-prod
332×log1p-expm1-u
331×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
16817
289017
Stop Event
1×node limit
Counts
1 → 73
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
Outputs
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) 2)) (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 (expm1.f64 x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (sqrt.f64 (pow.f64 x -2)))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (/.f64 (expm1.f64 x) x) (log.f64 (E.f64)))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 4)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (*.f64 (/.f64 1 x) (/.f64 (expm1.f64 x) x))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x -1/2) (pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (/.f64 (cbrt.f64 x) (expm1.f64 x)) -1))
(*.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) (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 (pow.f64 1 1/3) (/.f64 (expm1.f64 x) x))
(*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2) (expm1.f64 x)) 1/3) (cbrt.f64 (/.f64 1 x)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2) 1/3) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) -1) (pow.f64 (/.f64 x (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -1/2) -1) (pow.f64 (/.f64 x (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2))) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) -1) (pow.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) 1) -1) (pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1) (pow.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2) (expm1.f64 x))) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 4)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (expm1.f64 x) x) (expm1.f64 x))) (pow.f64 x -1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2) 1/2)
(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)
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 x) x)))
(pow.f64 (/.f64 (/.f64 x (expm1.f64 x)) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x)))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 x)) x))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 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)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(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))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))

eval16.0ms (0.4%)

Compiler

Compiled 888 to 384 computations (56.8% saved)

prune13.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New80585
Fresh000
Picked011
Done000
Total80686
Accuracy
100.0%
Counts
86 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
▶72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
▶68.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
▶57.1%
(+.f64 1 (*.f64 1/2 x))
▶57.5%
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
▶56.8%
1
Compiler

Compiled 89 to 65 computations (27% saved)

localize286.0ms (7.6%)

Localize:

Found 8 expressions with local error:

NewAccuracyProgram
✓99.9%
(/.f64 (sqrt.f64 (expm1.f64 x)) x)
✓99.8%
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
✓99.9%
(*.f64 x (+.f64 1/2 (*.f64 1/6 x)))
✓99.7%
(*.f64 1/6 x)
✓100.0%
(+.f64 1/6 (*.f64 1/24 x))
✓100.0%
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x)))))
✓99.8%
(*.f64 x (+.f64 1/6 (*.f64 1/24 x)))
✓99.7%
(*.f64 1/24 x)
Compiler

Compiled 115 to 76 computations (33.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 161.0ms
Operation ival-mult, time spent: 67.0ms, 41.0% of total-time
Operation ival-add, time spent: 40.0ms, 25.0% of total-time
Operation composed, time spent: 16.0ms, 10.0% of total-time
Operation const, time spent: 12.0ms, 7.0% of total-time
Operation ival-exp, time spent: 10.0ms, 6.0% of total-time
Operation ival-sqrt, time spent: 9.0ms, 6.0% of total-time
Operation ival-sub, time spent: 4.0ms, 2.0% of total-time
Operation ival-div, time spent: 3.0ms, 2.0% of total-time

series24.0ms (0.6%)

Counts
8 → 61
Calls

24 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(+.f64 1/6 (*.f64 1/24 x))
2.0ms
x
@inf
(/.f64 (sqrt.f64 (expm1.f64 x)) x)
1.0ms
x
@-inf
(*.f64 x (+.f64 1/6 (*.f64 1/24 x)))
1.0ms
x
@-inf
(/.f64 (sqrt.f64 (expm1.f64 x)) x)
1.0ms
x
@0
(/.f64 (sqrt.f64 (expm1.f64 x)) x)

rewrite173.0ms (4.6%)

Algorithm
1×batch-egg-rewrite
Rules
1910×prod-diff
843×log1p-expm1-u
340×associate-*r*
206×associate-*l*
146×expm1-log1p-u
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021164
1322144
24791144
Stop Event
1×node limit
Counts
8 → 201
Calls
Call 1
Inputs
(*.f64 1/24 x)
(*.f64 x (+.f64 1/6 (*.f64 1/24 x)))
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x)))))
(+.f64 1/6 (*.f64 1/24 x))
(*.f64 1/6 x)
(*.f64 x (+.f64 1/2 (*.f64 1/6 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (sqrt.f64 (expm1.f64 x)) x)
Outputs
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/24 x))) 1)
(pow.f64 (*.f64 1/24 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/24 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/24 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/24 x)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/576))
(log.f64 (pow.f64 (exp.f64 1/24) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/24 x))))
(cbrt.f64 (pow.f64 (*.f64 1/24 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/24 x)))
(log1p.f64 (expm1.f64 (*.f64 1/24 x)))
(exp.f64 (log.f64 (*.f64 1/24 x)))
(exp.f64 (*.f64 (log.f64 (*.f64 1/24 x)) 1))
(+.f64 (*.f64 x 1/6) (*.f64 1/24 (pow.f64 x 2)))
(+.f64 (*.f64 x 1/6) (*.f64 (*.f64 1/24 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 x 1/6))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 1/24 x 1/6)))) 1)
(/.f64 (+.f64 (*.f64 1/216 (pow.f64 x 3)) (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 3)) (+.f64 (*.f64 (pow.f64 x 2) 1/36) (-.f64 (*.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 2))) (*.f64 (*.f64 x 1/6) (*.f64 1/24 (pow.f64 x 2))))))
(/.f64 (-.f64 (*.f64 (pow.f64 x 2) 1/36) (*.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 2)))) (-.f64 (*.f64 x 1/6) (*.f64 1/24 (pow.f64 x 2))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216)) (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x))))
(/.f64 (*.f64 x (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576))) (+.f64 1/6 (*.f64 -1/24 x)))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216) x) (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x))))
(/.f64 (*.f64 (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576)) x) (+.f64 1/6 (*.f64 -1/24 x)))
(pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 1/24 x 1/6))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 1/24 x 1/6))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 1/24 x 1/6)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 1/24 x 1/6)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 1/24 x 1/6))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 1/24 x 1/6))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 1/24 x 1/6))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 1/24 x 1/6))) 1))
(fma.f64 x 1/6 (*.f64 1/24 (pow.f64 x 2)))
(fma.f64 1/6 x (*.f64 1/24 (pow.f64 x 2)))
(fma.f64 1 (*.f64 x 1/6) (*.f64 1/24 (pow.f64 x 2)))
(fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 1/36)) (cbrt.f64 (*.f64 x 1/6)) (*.f64 1/24 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 (*.f64 x 1/6)) (sqrt.f64 (*.f64 x 1/6)) (*.f64 1/24 (pow.f64 x 2)))
(+.f64 (*.f64 x 1/2) (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)))
(+.f64 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)) (*.f64 x 1/2))
(+.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)) (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2))) (*.f64 (*.f64 x 1/2) (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)) (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)))) (-.f64 (*.f64 x 1/2) (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 3) 1/8)) (+.f64 1/4 (*.f64 (*.f64 x (fma.f64 1/24 x 1/6)) (-.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 1/2))))
(/.f64 (*.f64 x (-.f64 1/4 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 2))) (-.f64 1/2 (*.f64 x (fma.f64 1/24 x 1/6))))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 3) 1/8) x) (+.f64 1/4 (*.f64 (*.f64 x (fma.f64 1/24 x 1/6)) (-.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 1/2))))
(/.f64 (*.f64 (-.f64 1/4 (pow.f64 (*.f64 x (fma.f64 1/24 x 1/6)) 2)) x) (-.f64 1/2 (*.f64 x (fma.f64 1/24 x 1/6))))
(pow.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (fma.f64 1/24 x 1/6) 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x (fma.f64 1/24 x 1/6) 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 1/24 x 1/6) 1/2))) 1))
(fma.f64 x 1/2 (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 (fma.f64 1/24 x 1/6) (pow.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/24 x 1/6))) 1)
(-.f64 (/.f64 1/36 (+.f64 1/6 (*.f64 -1/24 x))) (/.f64 (*.f64 (pow.f64 x 2) 1/576) (+.f64 1/6 (*.f64 -1/24 x))))
(*.f64 (fma.f64 1/24 x 1/6) 1)
(*.f64 1 (fma.f64 1/24 x 1/6))
(*.f64 (cbrt.f64 (fma.f64 1/24 x 1/6)) (pow.f64 (cbrt.f64 (fma.f64 1/24 x 1/6)) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/24 x 1/6)) 2) (cbrt.f64 (fma.f64 1/24 x 1/6)))
(*.f64 (sqrt.f64 (fma.f64 1/24 x 1/6)) (sqrt.f64 (fma.f64 1/24 x 1/6)))
(*.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216) (/.f64 1 (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x)))))
(*.f64 (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576)) (/.f64 1 (+.f64 1/6 (*.f64 -1/24 x))))
(/.f64 1 (/.f64 (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x))) (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216)))
(/.f64 1 (/.f64 (+.f64 1/6 (*.f64 -1/24 x)) (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576))))
(/.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216) (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x))))
(/.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216) (+.f64 (*.f64 (pow.f64 x 2) 1/576) (-.f64 1/36 (*.f64 1/144 x))))
(/.f64 (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576)) (+.f64 1/6 (*.f64 -1/24 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) 1/216)) (neg.f64 (+.f64 1/36 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 1/144 x)))))
(/.f64 (neg.f64 (-.f64 1/36 (*.f64 (pow.f64 x 2) 1/576))) (neg.f64 (+.f64 1/6 (*.f64 -1/24 x))))
(/.f64 (-.f64 (*.f64 (pow.f64 x 2) 1/576) 1/36) (-.f64 (*.f64 1/24 x) 1/6))
(pow.f64 (fma.f64 1/24 x 1/6) 1)
(pow.f64 (cbrt.f64 (fma.f64 1/24 x 1/6)) 3)
(pow.f64 (pow.f64 (fma.f64 1/24 x 1/6) 3) 1/3)
(pow.f64 (sqrt.f64 (fma.f64 1/24 x 1/6)) 2)
(sqrt.f64 (pow.f64 (fma.f64 1/24 x 1/6) 2))
(log.f64 (exp.f64 (fma.f64 1/24 x 1/6)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/24 x 1/6))))
(cbrt.f64 (pow.f64 (fma.f64 1/24 x 1/6) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/24 x 1/6)))
(log1p.f64 (expm1.f64 (fma.f64 1/24 x 1/6)))
(exp.f64 (log.f64 (fma.f64 1/24 x 1/6)))
(exp.f64 (*.f64 (log.f64 (fma.f64 1/24 x 1/6)) 1))
(fma.f64 1/24 x 1/6)
(fma.f64 x 1/24 1/6)
(fma.f64 1 (*.f64 1/24 x) 1/6)
(fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 1/576)) (cbrt.f64 (*.f64 1/24 x)) 1/6)
(fma.f64 (sqrt.f64 (*.f64 1/24 x)) (sqrt.f64 (*.f64 1/24 x)) 1/6)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x 1/6))) 1)
(pow.f64 (*.f64 x 1/6) 1)
(pow.f64 (cbrt.f64 (*.f64 x 1/6)) 3)
(pow.f64 (*.f64 1/216 (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x 1/6)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/36))
(log.f64 (pow.f64 (exp.f64 1/6) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/6))))
(cbrt.f64 (*.f64 1/216 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x 1/6)))
(log1p.f64 (expm1.f64 (*.f64 x 1/6)))
(exp.f64 (log.f64 (*.f64 x 1/6)))
(exp.f64 (*.f64 (log.f64 (*.f64 x 1/6)) 1))
(+.f64 (*.f64 x 1/2) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 x 1/2))
(+.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 1/6 (pow.f64 x 2)) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/6 (pow.f64 x 2))) (*.f64 (*.f64 x 1/2) (*.f64 1/6 (pow.f64 x 2))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/6 (pow.f64 x 2)))) (-.f64 (*.f64 x 1/2) (*.f64 1/6 (pow.f64 x 2))))
(/.f64 (*.f64 x (+.f64 (*.f64 1/216 (pow.f64 x 3)) 1/8)) (+.f64 1/4 (-.f64 (*.f64 (pow.f64 x 2) 1/36) (*.f64 1/12 x))))
(/.f64 (*.f64 x (-.f64 1/4 (*.f64 (pow.f64 x 2) 1/36))) (+.f64 1/2 (*.f64 -1/6 x)))
(/.f64 (*.f64 (+.f64 (*.f64 1/216 (pow.f64 x 3)) 1/8) x) (+.f64 1/4 (-.f64 (*.f64 (pow.f64 x 2) 1/36) (*.f64 1/12 x))))
(/.f64 (*.f64 (-.f64 1/4 (*.f64 (pow.f64 x 2) 1/36)) x) (+.f64 1/2 (*.f64 -1/6 x)))
(pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/6 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 1/6 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 1))
(fma.f64 x 1/2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (*.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x)))) (neg.f64 x))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x))) (neg.f64 x))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (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)
(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))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3/2) (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 3) (pow.f64 (expm1.f64 x) 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x))) 1)
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 1)
(*.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)) (cbrt.f64 (/.f64 (expm1.f64 x) (pow.f64 x 2))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (pow.f64 x 2))) (cbrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (/.f64 (pow.f64 (expm1.f64 x) 1/4) x))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (*.f64 (pow.f64 (expm1.f64 x) 1/4) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)) (sqrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) 1) (/.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) x))
(*.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(*.f64 (/.f64 (pow.f64 (expm1.f64 x) 1/4) 1) (/.f64 (pow.f64 (expm1.f64 x) 1/4) x))
(*.f64 (/.f64 (pow.f64 (expm1.f64 x) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (expm1.f64 x) 1/4) (cbrt.f64 x)))
(pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)) 2)
(pow.f64 (/.f64 x (sqrt.f64 (expm1.f64 x))) -1)
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) x))
(sqrt.f64 (/.f64 (expm1.f64 x) (pow.f64 x 2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) 3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3/2) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x)) 1))

eval98.0ms (2.6%)

Compiler

Compiled 3840 to 2728 computations (29% saved)

prune43.0ms (1.2%)

Pruning

8 alts after pruning (2 fresh and 6 done)

PrunedKeptTotal
New2602262
Fresh000
Picked055
Done011
Total2608268
Accuracy
100.0%
Counts
268 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
▶72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))))))
▶71.6%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
✓68.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
✓57.1%
(+.f64 1 (*.f64 1/2 x))
✓57.5%
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
✓56.8%
1
Compiler

Compiled 77 to 57 computations (26% saved)

localize275.0ms (7.3%)

Localize:

Found 7 expressions with local error:

NewAccuracyProgram
✓99.9%
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x)))))))
✓99.6%
(*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x)))))
✓99.5%
(*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))
✓99.4%
(*.f64 1/6 (/.f64 1 x))
✓99.9%
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x))))
✓99.8%
(*.f64 x (*.f64 1/24 x))
✓99.5%
(*.f64 1/24 x)
Compiler

Compiled 126 to 94 computations (25.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 163.0ms
Operation ival-add, time spent: 83.0ms, 51.0% of total-time
Operation ival-mult, time spent: 57.0ms, 35.0% of total-time
Operation ival-div, time spent: 18.0ms, 11.0% of total-time
Operation const, time spent: 5.0ms, 3.0% of total-time

series17.0ms (0.5%)

Counts
7 → 66
Calls

21 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x))))
1.0ms
x
@0
(*.f64 x (*.f64 1/24 x))
1.0ms
x
@-inf
(*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))
1.0ms
x
@-inf
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x))))
1.0ms
x
@0
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x))))

rewrite161.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
1870×prod-diff
961×log1p-expm1-u
346×associate-*r*
208×associate-*l*
139×expm1-log1p-u
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020181
1314164
24533164
Stop Event
1×node limit
Counts
7 → 146
Calls
Call 1
Inputs
(*.f64 1/24 x)
(*.f64 x (*.f64 1/24 x))
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x))))
(*.f64 1/6 (/.f64 1 x))
(*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))
(*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x)))))
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x)))))))
Outputs
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/24 x))) 1)
(pow.f64 (*.f64 1/24 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/24 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/24 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/24 x)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/576))
(log.f64 (pow.f64 (exp.f64 x) 1/24))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/24 x))))
(cbrt.f64 (pow.f64 (*.f64 1/24 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/24 x)))
(log1p.f64 (expm1.f64 (*.f64 1/24 x)))
(exp.f64 (log.f64 (*.f64 1/24 x)))
(exp.f64 (*.f64 (log.f64 (*.f64 1/24 x)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/24 (pow.f64 x 2)))) 1)
(pow.f64 (*.f64 1/24 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/24 (pow.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/24 (pow.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 2))
(log.f64 (exp.f64 (*.f64 1/24 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/24 (pow.f64 x 2)))))
(cbrt.f64 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 1/24 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 1/24 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/24 (pow.f64 x 2))))
(exp.f64 (*.f64 (log.f64 (*.f64 1/24 (pow.f64 x 2))) 1))
(+.f64 (*.f64 x (*.f64 1/24 (pow.f64 x 2))) (*.f64 x 1/2))
(+.f64 (*.f64 x 1/2) (*.f64 x (*.f64 1/24 (pow.f64 x 2))))
(+.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 x (*.f64 1/24 (pow.f64 x 2))) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 x (*.f64 1/24 (pow.f64 x 2))) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 x (*.f64 1/24 (pow.f64 x 2))) (*.f64 x (*.f64 1/24 (pow.f64 x 2)))) (*.f64 (*.f64 x 1/2) (*.f64 x (*.f64 1/24 (pow.f64 x 2)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 x (*.f64 1/24 (pow.f64 x 2))) (*.f64 x (*.f64 1/24 (pow.f64 x 2))))) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 1/24 (pow.f64 x 2)))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 3) 1/8)) (+.f64 1/4 (*.f64 (*.f64 1/24 (pow.f64 x 2)) (-.f64 (*.f64 1/24 (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 x (-.f64 1/4 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 2))) (-.f64 1/2 (*.f64 1/24 (pow.f64 x 2))))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 3) 1/8) x) (+.f64 1/4 (*.f64 (*.f64 1/24 (pow.f64 x 2)) (-.f64 (*.f64 1/24 (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 (-.f64 1/4 (pow.f64 (*.f64 1/24 (pow.f64 x 2)) 2)) x) (-.f64 1/2 (*.f64 1/24 (pow.f64 x 2))))
(pow.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x (*.f64 1/24 x) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x (*.f64 1/24 x) 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x (*.f64 1/24 x) 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 1/24 x) 1/2))) 1))
(fma.f64 x 1/2 (*.f64 x (*.f64 1/24 (pow.f64 x 2))))
(fma.f64 1/2 x (*.f64 x (*.f64 1/24 (pow.f64 x 2))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1/6 x))) 1)
(/.f64 1/6 x)
(/.f64 1 (/.f64 x 1/6))
(/.f64 -1/6 (neg.f64 x))
(/.f64 (/.f64 1/6 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (/.f64 1/6 (sqrt.f64 x)) (sqrt.f64 x))
(pow.f64 (/.f64 1/6 x) 1)
(pow.f64 (cbrt.f64 (/.f64 1/6 x)) 3)
(pow.f64 (/.f64 1/216 (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (/.f64 1/6 x)) 2)
(sqrt.f64 (/.f64 1/36 (pow.f64 x 2)))
(log.f64 (exp.f64 (/.f64 1/6 x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1/6 x))))
(cbrt.f64 (/.f64 1/216 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 1/6 x)))
(log1p.f64 (expm1.f64 (/.f64 1/6 x)))
(exp.f64 (log.f64 (/.f64 1/6 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 1/6 x)) 1))
(+.f64 (*.f64 1/24 x) (*.f64 x (/.f64 1/6 x)))
(+.f64 (*.f64 1/24 x) (*.f64 (*.f64 x (/.f64 1/6 x)) 1))
(+.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 1/24 x))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 1/24 x) 3) (pow.f64 (*.f64 x (/.f64 1/6 x)) 3)) (+.f64 (*.f64 (pow.f64 x 2) 1/576) (-.f64 (*.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 x (/.f64 1/6 x))) (*.f64 (*.f64 1/24 x) (*.f64 x (/.f64 1/6 x))))))
(/.f64 (-.f64 (*.f64 (pow.f64 x 2) 1/576) (*.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 x (/.f64 1/6 x)))) (-.f64 (*.f64 1/24 x) (*.f64 x (/.f64 1/6 x))))
(/.f64 (*.f64 x (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824)) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 x (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2)))) (-.f64 1/24 (/.f64 1/6 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824) x) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2))) x) (-.f64 1/24 (/.f64 1/6 x)))
(pow.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))) 2))
(log.f64 (pow.f64 (exp.f64 (+.f64 1/24 (/.f64 1/6 x))) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x))) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 1/24 (/.f64 1/6 x)) 3)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 1/24 (/.f64 1/6 x)) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))
(exp.f64 (log.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))) 1))
(fma.f64 1/24 x (*.f64 x (/.f64 1/6 x)))
(fma.f64 x 1/24 (*.f64 x (/.f64 1/6 x)))
(fma.f64 1 (*.f64 1/24 x) (*.f64 x (/.f64 1/6 x)))
(fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 1/576)) (cbrt.f64 (*.f64 1/24 x)) (*.f64 x (/.f64 1/6 x)))
(fma.f64 (sqrt.f64 (*.f64 1/24 x)) (sqrt.f64 (*.f64 1/24 x)) (*.f64 x (/.f64 1/6 x)))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 x (*.f64 x (/.f64 1/6 x))))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 1/6 x)))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 (*.f64 x (/.f64 1/6 x)) x))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 (/.f64 1/6 x) (pow.f64 x 2)))
(+.f64 (*.f64 (pow.f64 x 2) (/.f64 1/6 x)) (*.f64 1/24 (pow.f64 x 2)))
(+.f64 (*.f64 (/.f64 1/6 x) (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)))) 1)
(/.f64 (*.f64 (pow.f64 x 2) (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824)) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 (pow.f64 x 2) (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2)))) (-.f64 1/24 (/.f64 1/6 x)))
(pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 (+.f64 1/24 (/.f64 1/6 x)))) 2)
(sqrt.f64 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) (+.f64 1/24 (/.f64 1/6 x))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)))))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))) 1))
(+.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))))
(+.f64 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))) (*.f64 x 1/2))
(+.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))) (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x)))) (*.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))) (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))))) (-.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x)))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 3) 1/8)) (+.f64 1/4 (*.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) (-.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 x (-.f64 1/4 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 2))) (-.f64 1/2 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 3) 1/8) x) (+.f64 1/4 (*.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) (-.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 (-.f64 1/4 (pow.f64 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2)) 2)) x) (-.f64 1/2 (*.f64 (+.f64 1/24 (/.f64 1/6 x)) (pow.f64 x 2))))
(pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 1/24 (/.f64 1/6 x)) 1/2))) 1))
(fma.f64 x 1/2 (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))))
(fma.f64 1/2 x (*.f64 (pow.f64 x 3) (+.f64 1/24 (/.f64 1/6 x))))

eval102.0ms (2.7%)

Compiler

Compiled 3581 to 2848 computations (20.5% saved)

prune26.0ms (0.7%)

Pruning

8 alts after pruning (1 fresh and 7 done)

PrunedKeptTotal
New2111212
Fresh000
Picked112
Done066
Total2128220
Accuracy
100.0%
Counts
220 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
▶72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))))
✓71.6%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
✓68.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
✓57.1%
(+.f64 1 (*.f64 1/2 x))
✓57.5%
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
✓56.8%
1
Compiler

Compiled 75 to 55 computations (26.7% saved)

localize112.0ms (3%)

Localize:

Found 4 expressions with local error:

NewAccuracyProgram
✓99.9%
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))))
✓99.6%
(*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))
✓99.5%
(*.f64 x (+.f64 1/24 (/.f64 1/6 x)))
✓99.4%
(/.f64 1/6 x)
Compiler

Compiled 70 to 51 computations (27.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.0ms
Operation ival-div, time spent: 18.0ms, 32.0% of total-time
Operation ival-add, time spent: 18.0ms, 32.0% of total-time
Operation ival-mult, time spent: 18.0ms, 32.0% of total-time
Operation const, time spent: 3.0ms, 5.0% of total-time

series7.0ms (0.2%)

Counts
4 → 36
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))))
1.0ms
x
@0
(/.f64 1/6 x)
1.0ms
x
@-inf
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))))
1.0ms
x
@-inf
(*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))
1.0ms
x
@0
(*.f64 x (+.f64 1/24 (/.f64 1/6 x)))

rewrite120.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
1110×prod-diff
1071×log1p-expm1-u
1071×expm1-log1p-u
216×associate-*r*
120×associate-*l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014118
1195108
22954108
Stop Event
1×node limit
Counts
4 → 96
Calls
Call 1
Inputs
(/.f64 1/6 x)
(*.f64 x (+.f64 1/24 (/.f64 1/6 x)))
(*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))
(*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x))))))
Outputs
(-.f64 (exp.f64 (log1p.f64 (/.f64 1/6 x))) 1)
(*.f64 1/6 (/.f64 1 x))
(*.f64 (/.f64 1/6 x) 1)
(*.f64 1 (/.f64 1/6 x))
(*.f64 (cbrt.f64 (/.f64 1/6 x)) (pow.f64 (cbrt.f64 (/.f64 1/6 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 1/6 x)) 2) (cbrt.f64 (/.f64 1/6 x)))
(*.f64 (sqrt.f64 (/.f64 1/6 x)) (sqrt.f64 (/.f64 1/6 x)))
(*.f64 -1/6 (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1/6 x) 1)
(pow.f64 (cbrt.f64 (/.f64 1/6 x)) 3)
(pow.f64 (/.f64 1/216 (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (/.f64 1/6 x)) 2)
(pow.f64 (*.f64 x 6) -1)
(neg.f64 (/.f64 -1/6 x))
(sqrt.f64 (/.f64 1/36 (pow.f64 x 2)))
(log.f64 (exp.f64 (/.f64 1/6 x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1/6 x))))
(cbrt.f64 (/.f64 1/216 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 1/6 x)))
(log1p.f64 (expm1.f64 (/.f64 1/6 x)))
(exp.f64 (log.f64 (/.f64 1/6 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 1/6 x)) 1))
(+.f64 (*.f64 x 1/24) (*.f64 x (/.f64 1/6 x)))
(+.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 x 1/24))
(+.f64 (*.f64 (*.f64 x 1/24) 1) (*.f64 (*.f64 x (/.f64 1/6 x)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/24) 3) (pow.f64 (*.f64 x (/.f64 1/6 x)) 3)) (+.f64 (*.f64 (*.f64 x 1/24) (*.f64 x 1/24)) (-.f64 (*.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 x (/.f64 1/6 x))) (*.f64 (*.f64 x 1/24) (*.f64 x (/.f64 1/6 x))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/24) (*.f64 x 1/24)) (*.f64 (*.f64 x (/.f64 1/6 x)) (*.f64 x (/.f64 1/6 x)))) (-.f64 (*.f64 x 1/24) (*.f64 x (/.f64 1/6 x))))
(/.f64 (*.f64 x (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824)) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 x (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2)))) (-.f64 1/24 (/.f64 1/6 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824) x) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2))) x) (-.f64 1/24 (/.f64 1/6 x)))
(pow.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 (/.f64 1/6 x) 1/24)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 (/.f64 1/6 x) 1/24) 3)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1/6 x) 1/24) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))))
(exp.f64 (log.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 (/.f64 1/6 x) 1/24))) 1))
(fma.f64 x 1/24 (*.f64 x (/.f64 1/6 x)))
(fma.f64 1/24 x (*.f64 x (/.f64 1/6 x)))
(+.f64 (*.f64 x (*.f64 x 1/24)) (*.f64 x (*.f64 x (/.f64 1/6 x))))
(+.f64 (*.f64 (pow.f64 x 2) (/.f64 1/6 x)) (*.f64 (pow.f64 x 2) 1/24))
(+.f64 (*.f64 (pow.f64 x 2) 1/24) (*.f64 (pow.f64 x 2) (/.f64 1/6 x)))
(+.f64 (*.f64 (*.f64 x 1/24) x) (*.f64 (*.f64 x (/.f64 1/6 x)) x))
(+.f64 (*.f64 (/.f64 1/6 x) (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 2)))
(+.f64 (*.f64 1/24 (pow.f64 x 2)) (*.f64 (/.f64 1/6 x) (pow.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)))) 1)
(/.f64 (*.f64 (pow.f64 x 2) (+.f64 (/.f64 1/216 (pow.f64 x 3)) 1/13824)) (+.f64 1/576 (-.f64 (/.f64 1/36 (pow.f64 x 2)) (/.f64 1/144 x))))
(/.f64 (*.f64 (pow.f64 x 2) (-.f64 1/576 (/.f64 1/36 (pow.f64 x 2)))) (-.f64 1/24 (/.f64 1/6 x)))
(pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 (+.f64 (/.f64 1/6 x) 1/24))) 2)
(sqrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) (+.f64 (/.f64 1/6 x) 1/24)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)))))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))) 1))
(+.f64 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)) (*.f64 x 1/2))
(+.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)))
(+.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24))) (*.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24))))))
(/.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)))) (-.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 3) 1/8)) (+.f64 1/4 (*.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) (-.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 x (-.f64 1/4 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 2))) (-.f64 1/2 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 3) 1/8) x) (+.f64 1/4 (*.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) (-.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 1/2))))
(/.f64 (*.f64 (-.f64 1/4 (pow.f64 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2)) 2)) x) (-.f64 1/2 (*.f64 (+.f64 (/.f64 1/6 x) 1/24) (pow.f64 x 2))))
(pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 (pow.f64 x 2) (+.f64 (/.f64 1/6 x) 1/24) 1/2))) 1))
(fma.f64 x 1/2 (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)))
(fma.f64 1/2 x (*.f64 (pow.f64 x 3) (+.f64 (/.f64 1/6 x) 1/24)))

eval92.0ms (2.5%)

Compiler

Compiled 2452 to 1942 computations (20.8% saved)

prune21.0ms (0.6%)

Pruning

8 alts after pruning (0 fresh and 8 done)

PrunedKeptTotal
New1320132
Fresh000
Picked011
Done077
Total1328140
Accuracy
100.0%
Counts
140 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
✓72.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))))
✓71.6%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
✓68.1%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
✓57.1%
(+.f64 1 (*.f64 1/2 x))
✓57.5%
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
✓56.8%
1
Compiler

Compiled 166 to 119 computations (28.3% saved)

regimes13.0ms (0.3%)

Counts
10 → 1
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))))))
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
Outputs
(/.f64 (expm1.f64 x) x)
Calls

2 calls:

6.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
6.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 9 to 6 computations (33.3% saved)

regimes6.0ms (0.2%)

Counts
7 → 1
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (/.f64 1/6 x)))))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 x (+.f64 1/24 (*.f64 1/6 (/.f64 1 x))))))))
Outputs
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 1/24 x))))))
Calls

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
72.1%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
Outputs
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (*.f64 1/24 x)))))
Calls

1 calls:

4.0ms
x
Results
AccuracySegmentsBranch
71.6%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

Counts
3 → 1
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
Outputs
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 1/6 x))))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
68.1%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

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

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
57.1%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Stop Event
1×done
Counts
1 → 1
Calls
Call 1
Inputs
1
Outputs
1
Calls

1 calls:

4.0ms
x
Results
AccuracySegmentsBranch
56.8%1x
Compiler

Compiled 51 to 39 computations (23.5% saved)

soundness92.0ms (2.4%)

Rules
636×fma-define
382×fma-neg
222×times-frac
194×div-sub
128×distribute-rgt-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01588
14380
28880
324080
463080
597280
6134280
7158680
8165780
Stop Event
1×saturated
Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess72.0ms (1.9%)

Compiler

Compiled 148 to 106 computations (28.4% saved)

Profiling

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