Metrics for Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 14 to 11 computations (21.4% 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-add, 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

sample1.1s (63.5%)

Results

905.0ms	7249×	256	valid
128.0ms	1006×	256	infinite
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 368.0ms

Operation ival-mult, time spent: 135.0ms, 37.0% of total-time

Operation ival-sub, time spent: 112.0ms, 30.0% of total-time

Operation ival-add, time spent: 99.0ms, 27.0% of total-time

Operation const, time spent: 23.0ms, 6.0% of total-time

Bogosity

preprocess540.0ms (30.5%)

Algorithm

1×	egg-herbie

Rules

4330×	`fma-neg`
824×	`sub-neg`
800×	`fma-define`
534×	`unsub-neg`
478×	`associate-+l-`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`y`
-	-	`1/2`
-	-	`(*.f64 x (-.f64 y 1))`
-	-	`(-.f64 y 1)`
-	-	`918938533204673/1000000000000000`
-	-	`(*.f64 y 1/2)`
-	-	`1`
-	-	`(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))`
-	-	`(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)`

Iterations

Useful iterations: 13 (0.0ms)

Iter	Nodes	Cost
0	33	304
1	98	264
2	250	236
3	786	224
4	2305	224
5	3811	224
6	4343	224
7	4478	224
8	4504	224
9	4508	224
10	4561	224
11	4621	224
12	4645	224
13	4645	210
14	6612	210
15	6612	210
16	6612	210

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 (neg.f64 x) (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 x (-.f64 (neg.f64 y) 1)) (.f64 (neg.f64 y) 1/2)) 918938533204673/1000000000000000)
(neg.f64 (+.f64 (-.f64 (.f64 (neg.f64 x) (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000))
(neg.f64 (+.f64 (-.f64 (.f64 x (-.f64 (neg.f64 y) 1)) (.f64 (neg.f64 y) 1/2)) 918938533204673/1000000000000000))
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(+.f64 (-.f64 (.f64 (neg.f64 x) (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (.f64 (+.f64 y -1) (neg.f64 x)) (.f64 y 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 (+.f64 y -1) (neg.f64 x) (*.f64 y -1/2)))
(-.f64 918938533204673/1000000000000000 (fma.f64 x (+.f64 y -1) (*.f64 y 1/2)))
(fma.f64 x (-.f64 1 y) (fma.f64 y -1/2 918938533204673/1000000000000000))
(+.f64 x (fma.f64 y (-.f64 -1/2 x) 918938533204673/1000000000000000))
(+.f64 (-.f64 (.f64 x (-.f64 (neg.f64 y) 1)) (.f64 (neg.f64 y) 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (+.f64 (.f64 x (+.f64 (neg.f64 y) -1)) (.f64 y 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 x (fma.f64 -1 y -1) (*.f64 y 1/2)))
(fma.f64 x (-.f64 -1 y) (fma.f64 y 1/2 918938533204673/1000000000000000))
(-.f64 918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1/2) x))
(neg.f64 (+.f64 (-.f64 (.f64 (neg.f64 x) (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000))
(neg.f64 (+.f64 918938533204673/1000000000000000 (-.f64 (.f64 (+.f64 y -1) (neg.f64 x)) (.f64 y 1/2))))
(-.f64 -918938533204673/1000000000000000 (fma.f64 (+.f64 y -1) (neg.f64 x) (*.f64 y -1/2)))
(+.f64 (*.f64 x (+.f64 y -1)) (fma.f64 y 1/2 -918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1) (fma.f64 y 1/2 -918938533204673/1000000000000000))
(fma.f64 y (+.f64 x 1/2) (-.f64 -918938533204673/1000000000000000 x))
(neg.f64 (+.f64 (-.f64 (.f64 x (-.f64 (neg.f64 y) 1)) (.f64 (neg.f64 y) 1/2)) 918938533204673/1000000000000000))
(+.f64 (neg.f64 (+.f64 (.f64 x (+.f64 (neg.f64 y) -1)) (.f64 y 1/2))) -918938533204673/1000000000000000)
(-.f64 -918938533204673/1000000000000000 (fma.f64 x (fma.f64 -1 y -1) (*.f64 y 1/2)))
(neg.f64 (fma.f64 x (-.f64 -1 y) (fma.f64 y 1/2 918938533204673/1000000000000000)))
(fma.f64 x (+.f64 y 1) (fma.f64 y -1/2 -918938533204673/1000000000000000))
(+.f64 -918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1/2) x))
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y (+.f64 x -1)) (.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1) (*.f64 x -1/2)))
(fma.f64 y (+.f64 x -1) (fma.f64 x -1/2 918938533204673/1000000000000000))
(fma.f64 x -1/2 (fma.f64 y (+.f64 x -1) 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1/2) (-.f64 918938533204673/1000000000000000 y))

Compiler

Compiled 91 to 64 computations (29.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

Operation ival-mult, time spent: 21.0ms, 46.0% of total-time

Operation ival-sub, time spent: 18.0ms, 39.0% of total-time

Operation ival-add, time spent: 4.0ms, 9.0% of total-time

Operation const, time spent: 4.0ms, 9.0% of total-time

eval3.0ms (0.2%)

Compiler: Compiled 40 to 28 computations (30% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))

Compiler

Compiled 13 to 10 computations (23.1% saved)

localize55.0ms (3.1%)

Compiler: Compiled 35 to 25 computations (28.6% saved)
Precisions: Click to see histograms. Total time spent on operations: 20.0ms
Operation ival-mult, time spent: 10.0ms, 50.0% of total-time
Operation ival-sub, time spent: 4.0ms, 20.0% of total-time
Operation ival-add, time spent: 4.0ms, 20.0% of total-time
Operation const, time spent: 2.0ms, 10.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accuracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))

Compiler

Compiled 37 to 28 computations (24.3% saved)

regimes12.0ms (0.7%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Calls

4 calls:

4.0ms	x
3.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
2.0ms	y
2.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)`
100.0%	1	`(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))`

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`neg-mul-1`
18×	`unsub-neg`
16×	`*-commutative`
16×	`+-commutative`
12×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	31	40
2	45	40
3	56	40
4	73	40
5	96	40
6	97	40

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 x (+.f64 y -1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 13 to 10 computations (23.1% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess28.0ms (1.6%)

Compiler: Compiled 52 to 40 computations (23.1% saved)

analyze0.0ms (0%)

sample1.1s (63.5%)

preprocess540.0ms (30.5%)

eval3.0ms (0.2%)

prune1.0ms (0.1%)

localize55.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes12.0ms (0.7%)

simplify4.0ms (0.2%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess28.0ms (1.6%)

Profiling