Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

Time bar (total: 1.7s)

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 7 to 5 computations (28.6% saved)

sample858.0ms (51.5%)

Results
705.0ms6188×body256valid
142.0ms2068×body256infinite
Bogosity

preprocess51.0ms (3%)

Algorithm
1×egg-herbie
Rules
24×fma-def
17×associate-/r*
9×*-commutative
7×associate-*r*
4×associate-/l/
Problems
252×No Errors
4×(/.f64 1 (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
12639
24339
38739
412839
515239
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x x))
(/.f64 1 (*.f64 x x))
(/.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))
Outputs
(/.f64 1 (*.f64 x x))
(/.f64 1 (*.f64 x x))
(/.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))
(/.f64 1 (*.f64 x x))
Symmetry

(abs x)

Compiler

Compiled 18 to 10 computations (44.4% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.1%
(/.f64 1 (*.f64 x x))
▶99.1%
(/.f64 1 (*.f64 x x))
Compiler

Compiled 12 to 8 computations (33.3% saved)

localize20.0ms (1.2%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
99.1%
(/.f64 1 (*.f64 x x))
✓99.1%
(/.f64 1 (*.f64 x x))
Compiler

Compiled 12 to 6 computations (50% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite93.0ms (5.6%)

Algorithm
3×rewrite-once
1×batch-egg-rewrite
Rules
298×associate-*r/
282×associate-*l*
210×associate-*l/
191×unswap-sqr
183×unpow-prod-down
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0613
1247
2717
32497
411037
Stop Event
1×node limit
Counts
1 → 43
Calls
Call 1
Inputs
(/.f64 1 (*.f64 x x))
Outputs
-9
-8
-6
-4
-3
-2
-3/2
-1
-3/4
-1/2
-1/4
-1/8
-1/16
0
1/8
1/4
1/2
3/4
1
3/2
2
3
4
6
8
9
12
18
x
Calls

3 calls:

1.0ms
(/.f64 1 (*.f64 x x))
0.0ms
(/.f64 1 (*.f64 x x))
0.0ms
(/.f64 1 (*.f64 x x))

simplify74.0ms (4.4%)

Algorithm
1×egg-herbie
Rules
562×fma-def
440×associate-*r/
428×*-commutative
393×associate-/l*
333×associate-+r+
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
063407
187407
2268407
31061407
44068257
Stop Event
1×node limit
Counts
55 → 44
Calls
Call 1
Inputs
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
-9
-8
-6
-4
-3
-2
-3/2
-1
-3/4
-1/2
-1/4
-1/8
-1/16
0
1/8
1/4
1/2
3/4
1
3/2
2
3
4
6
8
9
12
18
(exp.f64 (log.f64 (/.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (/.f64 1 (*.f64 x x))))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 x x))) (sqrt.f64 (/.f64 1 (*.f64 x x))))
(log1p.f64 (expm1.f64 (/.f64 1 (*.f64 x x))))
(expm1.f64 (log1p.f64 (/.f64 1 (*.f64 x x))))
(*.f64 1 (/.f64 1 (*.f64 x x)))
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) (cbrt.f64 (/.f64 1 (*.f64 x x)))) (cbrt.f64 (/.f64 1 (*.f64 x x))))
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (*.f64 x x))) (/.f64 1 (*.f64 x x))))
(pow.f64 (/.f64 1 (*.f64 x x)) 1)
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (/.f32 1 (*.f32 (binary64->binary32 x) (binary64->binary32 x))))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (/.f32 1 (*.f32 (binary64->binary32 x) (binary64->binary32 x))))
Outputs
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
-9
-8
-6
-4
-3
-2
-3/2
-1
-3/4
-1/2
-1/4
-1/8
-1/16
0
1/8
1/4
1/2
3/4
1
3/2
2
3
4
6
8
9
12
18
(exp.f64 (log.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(log.f64 (exp.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 x x))) (sqrt.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(log1p.f64 (expm1.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(expm1.f64 (log1p.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(*.f64 1 (/.f64 1 (*.f64 x x)))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) (cbrt.f64 (/.f64 1 (*.f64 x x)))) (cbrt.f64 (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (*.f64 x x))) (/.f64 1 (*.f64 x x))))
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(pow.f64 (/.f64 1 (*.f64 x x)) 1)
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (pow.f64 x -2)))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (pow.f64 x -2)))
(binary32->binary64 (/.f32 1 (*.f32 (binary64->binary32 x) (binary64->binary32 x))))
(binary32->binary64 (/.f32 (/.f32 1 (binary64->binary32 x)) (binary64->binary32 x)))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (pow.f64 x -2)))
(binary32->binary64 (binary64->binary32 (/.f64 1 (*.f64 x x))))
(binary32->binary64 (binary64->binary32 (pow.f64 x -2)))
(binary32->binary64 (/.f32 1 (*.f32 (binary64->binary32 x) (binary64->binary32 x))))
(binary32->binary64 (/.f32 (/.f32 1 (binary64->binary32 x)) (binary64->binary32 x)))

eval6.0ms (0.4%)

Compiler

Compiled 163 to 106 computations (35% saved)

prune16.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New39544
Fresh000
Picked011
Done000
Total39645
Accuracy
100.0%
Counts
45 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
▶100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize19.0ms (1.1%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New000
Fresh044
Picked011
Done011
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
✓100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New000
Fresh044
Picked000
Done022
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
✓100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New000
Fresh044
Picked000
Done022
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(pow.f64 x -2)
✓99.1%
(/.f64 1 (*.f64 x x))
4.4%
18
4.4%
1/2
4.4%
1/8
28.9%
0
Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes64.0ms (3.8%)

Counts
6 → 1
Calls
Call 1
Inputs
0
1/8
1/2
18
(/.f64 1 (*.f64 x x))
(pow.f64 x -2)
Outputs
(pow.f64 x -2)
Calls

3 calls:

5.0ms
x
4.0ms
(/.f64 1 (*.f64 x x))
3.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 1 (*.f64 x x))
100.0%1(*.f64 x x)
Compiler

Compiled 25 to 17 computations (32% saved)

regimes14.0ms (0.9%)

Counts
5 → 1
Calls
Call 1
Inputs
0
1/8
1/2
18
(/.f64 1 (*.f64 x x))
Outputs
(/.f64 1 (*.f64 x x))
Calls

3 calls:

5.0ms
x
3.0ms
(*.f64 x x)
3.0ms
(/.f64 1 (*.f64 x x))
Results
AccuracySegmentsBranch
99.1%1x
99.1%1(/.f64 1 (*.f64 x x))
99.1%1(*.f64 x x)
Compiler

Compiled 22 to 15 computations (31.8% saved)

regimes12.0ms (0.7%)

Counts
4 → 2
Calls
Call 1
Inputs
0
1/8
1/2
18
Outputs
1/2
0
Calls

1 calls:

11.0ms
x
Results
AccuracySegmentsBranch
30.6%2x
Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes10.0ms (0.6%)

Counts
2 → 2
Calls
Call 1
Inputs
0
1/8
Outputs
1/8
0
Calls

1 calls:

9.0ms
x
Results
AccuracySegmentsBranch
30.6%2x
Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
0
Outputs
0
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
28.9%1x
Compiler

Compiled 4 to 3 computations (25% saved)

bsearch12.0ms (0.7%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
4.40629760698198e+76
6.898358916840948e+80
Results
11.0ms128×body256valid
Compiler

Compiled 58 to 55 computations (5.2% saved)

bsearch12.0ms (0.7%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
11.0ms
4.40629760698198e+76
6.898358916840948e+80
Results
10.0ms128×body256valid
Compiler

Compiled 58 to 55 computations (5.2% saved)

simplify10.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
3×1-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02043
12543
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(pow.f64 x -2)
(/.f64 1 (*.f64 x x))
(if (<=.f64 x 119999999999999992791711785436734146363018478165098748993720564156436311965696) 1/2 0)
(if (<=.f64 x 160000000000000007529621519344875134264953622525866092228459352558371992502272) 1/8 0)
0
Outputs
(pow.f64 x -2)
(/.f64 1 (*.f64 x x))
(if (<=.f64 x 119999999999999992791711785436734146363018478165098748993720564156436311965696) 1/2 0)
(if (<=.f64 x 160000000000000007529621519344875134264953622525866092228459352558371992502272) 1/8 0)
0
Compiler

Compiled 26 to 21 computations (19.2% saved)

soundness336.0ms (20.2%)

Rules
562×fma-def
440×associate-*r/
428×*-commutative
393×associate-/l*
333×associate-+r+
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
063407
187407
2268407
31061407
44068257
0613
1247
2717
32497
411037
0613
1247
2717
32497
411037
0613
1247
2717
32497
411037
Stop Event
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 55 to 38 computations (30.9% saved)

end0.0ms (0%)

preprocess45.0ms (2.7%)

Remove

(abs x)

Compiler

Compiled 76 to 56 computations (26.3% saved)

Profiling

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