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)

sample2.3s (83.7%)

Results

1.5s	6132×	body	256	valid
722.0ms	2124×	body	256	infinite

Bogosity

preprocess146.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

200×	`fma-def`
38×	`associate-r`
34×	`distribute-lft-neg-in`
24×	`associate-l`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	33	45
2	70	45
3	148	45
4	234	45
5	324	45
6	349	45
7	354	45
8	357	45

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)

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)

Symmetry

(abs x)

Compiler

Compiled 8 to 6 computations (25% saved)

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)
▶	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)

Compiler

Compiled 16 to 12 computations (25% saved)

localize25.0ms (0.9%)

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)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	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)

rewrite67.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1040×	`pow1`
1002×	`add-sqr-sqrt`
954×	`add-exp-log`
954×	`log1p-expm1-u`
954×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	121	13
2	1360	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 (.f64 x x) 2)

Outputs
(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
(pow.f64 (.f64 x (.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 x) (*.f64 x 2)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x 2))))
(exp.f64 (log.f64 (.f64 x (.f64 x 2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x 2))))

simplify54.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1438×	`log-prod`
1064×	`distribute-lft-in`
1000×	`distribute-rgt-in`
944×	`associate-r`
852×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	299
1	89	299
2	331	299
3	2358	299

Stop Event

1×	node limit

Counts

23 → 13

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 (+.f64 1 (.f64 x (.f64 x 2))) 1)
(pow.f64 (.f64 x (.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 x) (*.f64 x 2)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x 2))))
(exp.f64 (log.f64 (.f64 x (.f64 x 2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x 2))))

Outputs
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
(.f64 2 (.f64 x x))
(pow.f64 (.f64 x (.f64 x 2)) 1)
(.f64 2 (.f64 x x))
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3)
(.f64 2 (.f64 x x))
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 3) 1/3)
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(.f64 2 (.f64 x x))
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(.f64 2 (.f64 x x))
(log.f64 (pow.f64 (exp.f64 x) (*.f64 x 2)))
(.f64 2 (.f64 x x))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3))
(.f64 2 (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 x (.f64 x 2))))
(.f64 2 (.f64 x x))
(exp.f64 (log.f64 (.f64 x (.f64 x 2))))
(.f64 2 (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 x (.f64 x 2))))
(.f64 2 (.f64 x x))

eval13.0ms (0.5%)

Compiler: Compiled 118 to 95 computations (19.5% saved)

prune9.0ms (0.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	1	14

Accuracy

100.0%

Counts

14 → 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)

simplify40.0ms (1.5%)

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)

Iter	Nodes	Cost
0	8	19
1	14	19
2	18	19
3	21	19
4	24	19
5	27	19

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%)

preprocess92.0ms (3.3%)

Remove: (abs x)
Compiler: Compiled 48 to 36 computations (25% saved)

analyze0.0ms (0%)

sample2.3s (83.7%)

preprocess146.0ms (5.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize25.0ms (0.9%)

series1.0ms (0%)

rewrite67.0ms (2.4%)

simplify54.0ms (2%)

eval13.0ms (0.5%)

prune9.0ms (0.3%)

simplify40.0ms (1.5%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess92.0ms (3.3%)

Profiling