Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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. Total time spent on operations: 0.0ms

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.4s (69%)

Results

807.0ms	6271×	valid
434.0ms	1984×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 236.0ms

Operation ival-mult, time spent: 152.0ms, 64.0% of total-time

Operation ival-sub, time spent: 63.0ms, 27.0% of total-time

Operation const, time spent: 16.0ms, 7.0% of total-time

Operation backward-pass, time spent: 4.0ms, 2.0% of total-time

Bogosity

preprocess120.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-neg`
94×	`fma-define`
42×	`distribute-lft-neg-in`
36×	`associate-r`
30×	`associate-l`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (.f64 (.f64 x x) 2) 1)`
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(.f64 (.f64 x x) 2)`
-	-	`2`
-	-	`1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	88
1	41	88
2	90	88
3	193	84
4	302	84
5	380	84
6	395	84
7	397	84

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 48 to 28 computations (41.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

Operation ival-mult, time spent: 12.0ms, 70.0% of total-time

Operation ival-sub, time spent: 3.0ms, 17.0% of total-time

Operation const, time spent: 2.0ms, 12.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)

Compiler

Compiled 8 to 6 computations (25% saved)

localize182.0ms (8.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 (.f64 x x) 2)

Compiler

Compiled 20 to 11 computations (45% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

Operation ival-mult, time spent: 5.0ms, 64.0% of total-time

Operation ival-sub, time spent: 2.0ms, 26.0% of total-time

Operation const, time spent: 1.0ms, 13.0% of total-time

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x x) 2)
1.0ms	x	@	inf	(.f64 (.f64 x x) 2)
1.0ms	x	@	-inf	(.f64 (.f64 x x) 2)

rewrite222.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1012×	`associate-r`
904×	`associate-l`
542×	`unpow-prod-down`
316×	`log-prod`
312×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	67	16
2	734	16

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)))
(log1p.f64 (expm1.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))

simplify52.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-neg`
638×	`times-frac`
628×	`distribute-lft-out`
552×	`*-commutative`
500×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	86	850
1	210	832
2	595	815
3	2926	815

Stop Event

1×	node limit

Counts

37 → 32

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)))
(log1p.f64 (expm1.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))

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 (log.f64 (cbrt.f64 (exp.f64 (*.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 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))
(log1p.f64 (expm1.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))

eval13.0ms (0.7%)

Compiler: Compiled 468 to 412 computations (12% saved)

prune4.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	1	33

Accuracy

100.0%

Counts

33 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)

Compiler

Compiled 16 to 12 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`unsub-neg`
4×	`sub-neg`
4×	`*-commutative`
4×	`neg-mul-1`
4×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	19	25
2	23	25
3	26	25
4	29	25
5	32	25

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%)

preprocess32.0ms (1.5%)

Remove: (abs x)
Compiler: Compiled 64 to 48 computations (25% saved)

analyze0.0ms (0%)

sample1.4s (69%)

preprocess120.0ms (5.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize182.0ms (8.9%)

series2.0ms (0.1%)

rewrite222.0ms (10.9%)

simplify52.0ms (2.6%)

eval13.0ms (0.7%)

prune4.0ms (0.2%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess32.0ms (1.5%)

Profiling