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)

sample884.0ms (66.7%)

Results

598.0ms	6201×	body	256	valid
274.0ms	2055×	body	256	infinite

Bogosity

preprocess119.0ms (9%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-def`
45×	`associate-r`
33×	`*-commutative`
22×	`associate-l`
18×	`distribute-lft-in`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	38	63
2	68	63
3	160	63
4	282	63
5	372	63
6	394	63
7	403	63
8	406	63

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 2 (*.f64 x x) -1)
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (.f64 (.f64 x x) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 2 (*.f64 x x) -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 2 (*.f64 x x) -1)
(fma.f64 x (*.f64 x 2) -1)

Symmetry

(abs x)

Compiler

Compiled 28 to 17 computations (39.3% saved)

eval1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

prune1.0ms (0.1%)

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 (1.9%)

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 (0.1%)

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)

rewrite186.0ms (14.1%)

Algorithm

1×	batch-egg-rewrite

Rules

643×	`associate-r`
516×	`associate-l`
224×	`pow1`
208×	`add-exp-log`
202×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	67	16
2	737	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 (*.f64 (pow.f64 x 2) 2) 1) -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 (*.f64 (pow.f64 x 2) 2) 1) 1)
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) 1) (+.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 1))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) (+.f64 1 (+.f64 (*.f64 (pow.f64 x 2) 2) 1))))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(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 (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 (.f64 x (sqrt.f64 2))) 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))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 2) 2)))

simplify49.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

488×	`associate--l+`
394×	`*-commutative`
386×	`distribute-lft-out`
367×	`associate-/l*`
302×	`associate--r+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	894
1	198	882
2	589	866
3	3017	860

Stop Event

1×	node limit

Counts

37 → 34

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 (*.f64 (pow.f64 x 2) 2) 1) -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 (*.f64 (pow.f64 x 2) 2) 1) 1)
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) 1) (+.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 1))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) (+.f64 1 (+.f64 (*.f64 (pow.f64 x 2) 2) 1))))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(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 (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 (.f64 x (sqrt.f64 2))) 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))
(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 (*.f64 (pow.f64 x 2) 2) 1) -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 (+.f64 (*.f64 (pow.f64 x 2) 2) 1) 1)
(*.f64 2 (pow.f64 x 2))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) 1) (+.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 1))
(/.f64 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) 2) (.f64 2 (pow.f64 x 2))) (+.f64 (.f64 2 (pow.f64 x 2)) 2))
(/.f64 (fma.f64 2 (pow.f64 x 2) 2) (/.f64 (fma.f64 2 (pow.f64 x 2) 2) (*.f64 2 (pow.f64 x 2))))
(.f64 (/.f64 (.f64 (pow.f64 x 2) (fma.f64 2 (pow.f64 x 2) 2)) (fma.f64 x x 1)) 1)
(/.f64 (pow.f64 x 2) (/.f64 (fma.f64 x x 1) (fma.f64 2 (pow.f64 x 2) 2)))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 (pow.f64 x 2) 2) 1) (+.f64 (.f64 (pow.f64 x 2) 2) 1)) (+.f64 1 (+.f64 (*.f64 (pow.f64 x 2) 2) 1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 2 1) 3) -1) (fma.f64 (fma.f64 (pow.f64 x 2) 2 1) (fma.f64 (pow.f64 x 2) 2 1) (+.f64 (*.f64 2 (pow.f64 x 2)) 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) (fma.f64 2 (pow.f64 x 2) 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))))
(pow.f64 (*.f64 (pow.f64 x 2) 2) 1)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(*.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)
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(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))
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(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))
(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 (.f64 x (sqrt.f64 2))) 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))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 2) 2)))
(*.f64 2 (pow.f64 x 2))

eval13.0ms (1%)

Compiler: Compiled 502 to 436 computations (13.1% saved)

prune5.0ms (0.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	1	35

Accuracy

100.0%

Counts

35 → 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 (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`distribute-lft-neg-out`
2×	`sub-neg`
2×	`+-commutative`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	19	25
2	23	25
3	27	25
4	30	25
5	34	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%)

preprocess40.0ms (3%)

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

analyze0.0ms (0%)

sample884.0ms (66.7%)

preprocess119.0ms (9%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize25.0ms (1.9%)

series1.0ms (0.1%)

rewrite186.0ms (14.1%)

simplify49.0ms (3.7%)

eval13.0ms (1%)

prune5.0ms (0.4%)

simplify3.0ms (0.2%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess40.0ms (3%)

Profiling