Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

Time bar (total: 1.7s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions
Click to see histograms
Operation ival-sub, total time spent: 0.0ms
Operation ival-mult, total time spent: 0.0ms
Operation const, total time spent: 0.0ms

sample1.3s (77.6%)

Results
677.0ms6259×body256valid
650.0ms1997×body256infinite
Precisions
Click to see histograms
Operation ival-sub, total time spent: 59.0ms
Operation ival-mult, total time spent: 178.0ms
Operation const, total time spent: 25.0ms
Bogosity

preprocess86.0ms (5%)

Algorithm
1×egg-herbie
Rules
206×fma-def
42×distribute-lft-neg-in
36×associate-*r*
30×associate-*l*
26×distribute-rgt-neg-in
Problems
256×No Errors
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01688
14188
29088
319384
430284
538084
639584
739784
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (*.f64 (*.f64 x x) 2) 1)
(-.f64 (*.f64 (*.f64 x x) 2) 1)
(-.f64 (*.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 2) 1)
(neg.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 2) 1))
Outputs
(-.f64 (*.f64 (*.f64 x x) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (*.f64 (*.f64 x x) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (*.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)
(neg.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 2) 1))
(neg.f64 (fma.f64 (*.f64 x x) 2 -1))
(neg.f64 (fma.f64 x (*.f64 x 2) -1))
(fma.f64 x (*.f64 x -2) 1)
Symmetry

(abs x)

Compiler

Compiled 28 to 17 computations (39.3% saved)

Precisions
Click to see histograms
Operation ival-sub, total time spent: 3.0ms
Operation ival-mult, total time spent: 5.0ms
Operation const, total time spent: 1.0ms

eval0.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

prune2.0ms (0.1%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(-.f64 (*.f64 (*.f64 x x) 2) 1)
▶100.0%
(-.f64 (*.f64 (*.f64 x x) 2) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

localize35.0ms (2.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(*.f64 (*.f64 x x) 2)
Compiler

Compiled 20 to 11 computations (45% saved)

Precisions
Click to see histograms
Operation ival-sub, total time spent: 2.0ms
Operation ival-mult, total time spent: 5.0ms
Operation const, total time spent: 1.0ms

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite168.0ms (9.8%)

Algorithm
1×batch-egg-rewrite
Rules
1010×associate-*r*
904×associate-*l*
446×unpow-prod-down
316×log-prod
312×cbrt-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
16716
273216
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) 2)
Outputs
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) -1)
(+.f64 0 (*.f64 (pow.f64 x 2) 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) 1) (+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2)) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(fabs.f64 (*.f64 (pow.f64 x 2) 2))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 2)))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2))) 3))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 8)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 2) 2)))

simplify49.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
1174×times-frac
736×associate-*r/
612×distribute-lft-out
584×fma-def
506×fma-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
086850
1203832
2569815
32780815
Stop Event
1×node limit
Counts
37 → 31
Calls
Call 1
Inputs
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) -1)
(+.f64 0 (*.f64 (pow.f64 x 2) 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) 1) (+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2)) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(fabs.f64 (*.f64 (pow.f64 x 2) 2))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 2)))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2))) 3))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 8)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 2) 2)))
Outputs
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) -1)
(*.f64 2 (pow.f64 x 2))
(+.f64 0 (*.f64 (pow.f64 x 2) 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 2))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1)
(*.f64 2 (pow.f64 x 2))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) 3) -1) (fma.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) (+.f64 1 (*.f64 2 (pow.f64 x 2))) (+.f64 1 (+.f64 1 (*.f64 2 (pow.f64 x 2))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x 2) 1) 3)) (fma.f64 (fma.f64 2 (pow.f64 x 2) 1) (fma.f64 2 (pow.f64 x 2) 1) (+.f64 2 (*.f64 2 (pow.f64 x 2)))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x 2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x 2) 1) (fma.f64 2 (pow.f64 x 2) 2))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) (+.f64 1 (*.f64 (pow.f64 x 2) 2))) 1) (+.f64 (+.f64 1 (*.f64 (pow.f64 x 2) 2)) 1))
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2)) 3)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(*.f64 2 (pow.f64 x 2))
(fabs.f64 (*.f64 (pow.f64 x 2) 2))
(*.f64 2 (pow.f64 x 2))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 2)))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 2) 2))) 3))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 2))
(*.f64 2 (pow.f64 x 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 2) 2)))
(*.f64 2 (pow.f64 x 2))

eval14.0ms (0.8%)

Compiler

Compiled 449 to 395 computations (12% saved)

prune4.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New31031
Fresh000
Picked011
Done000
Total31132
Accuracy
100.0%
Counts
32 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(-.f64 (*.f64 (*.f64 x x) 2) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×unsub-neg
4×sub-neg
4×neg-mul-1
4×+-commutative
4×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
11925
22325
32625
42925
53225
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(-.f64 (*.f64 (*.f64 x x) 2) 1)
Outputs
(-.f64 (*.f64 (*.f64 x x) 2) 1)
(+.f64 (*.f64 (*.f64 x x) 2) -1)
Compiler

Compiled 8 to 6 computations (25% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess23.0ms (1.3%)

Remove

(abs x)

Compiler

Compiled 64 to 48 computations (25% saved)

Profiling

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