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)

sample772.0ms (37.4%)

Results

663.0ms	7246×	body	256	valid
98.0ms	1010×	body	256	infinite

Bogosity

preprocess353.0ms (17.1%)

Algorithm

1×	egg-herbie

Rules

4146×	`fma-def`
1176×	`fma-neg`
746×	`sub-neg`
546×	`unsub-neg`
452×	`associate-+l-`

Problems

256×

No Errors

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	28	163
1	80	141
2	203	119
3	606	115
4	1734	107
5	3675	107
6	4448	107
7	4688	107
8	4738	107
9	4742	107
10	4744	107
11	4774	107
12	4774	105
13	6401	105
14	6401	105
15	6401	105

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

Compiler

Compiled 52 to 37 computations (28.8% saved)

eval1.0ms (0.1%)

Compiler: Compiled 48 to 33 computations (31.3% saved)

prune2.0ms (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))
▶	100.0%	(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize40.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 x (+.f64 y -1))

Compiler

Compiled 35 to 25 computations (28.6% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(*.f64 x (+.f64 y -1))
1.0ms	y	@	-inf	(*.f64 x (+.f64 y -1))
0.0ms	x	@	0	(*.f64 x (+.f64 y -1))
0.0ms	x	@	inf	(*.f64 x (+.f64 y -1))
0.0ms	x	@	-inf	(*.f64 x (+.f64 y -1))

rewrite56.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1594×	`pow1`
1474×	`add-exp-log`
1474×	`log1p-expm1-u`
1474×	`expm1-log1p-u`
1448×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	153	13
2	1986	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(*.f64 x (+.f64 y -1))

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

simplify59.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-neg`
846×	`div-sub`
636×	`distribute-lft-neg-out`
580×	`associate-+r+`
560×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	710
1	217	688
2	792	676
3	3433	674

Stop Event

1×	node limit

Counts

46 → 34

Calls

Call 1

Inputs
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 x (-.f64 y 1))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(*.f64 x y)
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(*.f64 x y)
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (.f64 -1 x) (.f64 x y))
(+.f64 (*.f64 x y) (neg.f64 x))
(+.f64 (neg.f64 x) (*.f64 x y))
(+.f64 (.f64 (.f64 x y) 1) (*.f64 (neg.f64 x) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 y -1))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (neg.f64 x) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (*.f64 x y) (neg.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 x y) (neg.f64 x)))
(/.f64 (.f64 x (+.f64 -1 (pow.f64 y 3))) (fma.f64 y y (-.f64 1 (.f64 y -1))))
(/.f64 (*.f64 x (fma.f64 y y -1)) (+.f64 y 1))
(/.f64 (.f64 (+.f64 -1 (pow.f64 y 3)) x) (fma.f64 y y (-.f64 1 (.f64 y -1))))
(/.f64 (*.f64 (fma.f64 y y -1) x) (+.f64 y 1))
(pow.f64 (*.f64 x (+.f64 y -1)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 y -1))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 2))
(log.f64 (pow.f64 (exp.f64 (+.f64 y -1)) x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 y -1))))
(exp.f64 (log.f64 (*.f64 x (+.f64 y -1))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 y -1))))
(fma.f64 x y (neg.f64 x))
(fma.f64 y x (neg.f64 x))

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

eval10.0ms (0.5%)

Compiler: Compiled 572 to 364 computations (36.4% saved)

prune7.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Accuracy

100.0%

Counts

35 → 3

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))
▶	78.0%	(-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
▶	76.7%	(-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))
✓	100.0%	(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
▶	78.0%	(-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
▶	76.7%	(-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize54.0ms (2.6%)

Compiler: Compiled 49 to 31 computations (36.7% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accuracy

100.0%

Counts

3 → 3

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))

✓

78.0%

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

✓

76.7%

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

Compiler

Compiled 75 to 56 computations (25.3% saved)

regimes16.0ms (0.8%)

Counts

4 → 1

Calls

Call 1

Inputs
(-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))
(-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
(+.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	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
4.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
4.0ms	x
4.0ms	y

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 71 to 52 computations (26.8% saved)

regimes26.0ms (1.3%)

Counts

2 → 3

Calls

Call 1

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

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

Outputs

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

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

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

Calls

2 calls:

15.0ms	x
9.0ms	y

Results

Accuracy	Segments	Branch
85.7%	5	`x`
98.7%	3	`y`

Compiler

Compiled 25 to 18 computations (28% saved)

regimes6.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
76.7%	1	`x`
76.7%	1	`y`

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch37.0ms (1.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.8586943782581508e-15	8.887390747669008e-8
20.0ms	-1.3145021385756196e+21	-0.010080284814533654

Results

32.0ms	318×	body	256	valid
0.0ms	2×	body	256	infinite

Compiler

Compiled 478 to 374 computations (21.8% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

32×	`+-commutative`
28×	`sub-neg`
22×	`*-commutative`
20×	`neg-mul-1`
20×	`neg-sub0`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	127
1	52	127
2	78	127
3	106	119
4	119	119
5	122	119
6	123	119

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

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

(if (<=.f64 y -1) (-.f64 (*.f64 x y) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000)) (if (<=.f64 y 812247035053579/9444732965739290427392) (-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000)) (-.f64 (*.f64 x y) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))))

(-.f64 (neg.f64 x) (-.f64 (*.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)
(if (<=.f64 y -1) (-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000)) (if (<=.f64 y 812247035053579/9444732965739290427392) (-.f64 (neg.f64 x) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000)) (-.f64 (.f64 x y) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))))
(if (or (<=.f64 y -1) (not (<=.f64 y 812247035053579/9444732965739290427392))) (-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000)) (-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000)))
(if (or (<=.f64 y -1) (not (<=.f64 y 812247035053579/9444732965739290427392))) (-.f64 (.f64 x y) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000)) (-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y (neg.f64 1/2))) x))
(if (or (<=.f64 y -1) (not (<=.f64 y 812247035053579/9444732965739290427392))) (+.f64 (.f64 x y) (-.f64 918938533204673/1000000000000000 (.f64 y 1/2))) (-.f64 (-.f64 918938533204673/1000000000000000 (*.f64 y 1/2)) x))
(-.f64 (neg.f64 x) (-.f64 (*.f64 y 1/2) 918938533204673/1000000000000000))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y (neg.f64 1/2))) x)
(-.f64 (-.f64 918938533204673/1000000000000000 (*.f64 y 1/2)) x)

Compiler

Compiled 49 to 37 computations (24.5% saved)

soundness566.0ms (27.4%)

Rules

4146×	`fma-def`
1176×	`fma-neg`
880×	`fma-neg`
846×	`div-sub`
746×	`sub-neg`

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	28	163
1	80	141
2	203	119
3	606	115
4	1734	107
5	3675	107
6	4448	107
7	4688	107
8	4738	107
9	4742	107
10	4744	107
11	4774	107
12	4774	105
13	6401	105
14	6401	105
15	6401	105
0	74	710
1	217	688
2	792	676
3	3433	674

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 66 to 50 computations (24.2% saved)

end0.0ms (0%)

preprocess47.0ms (2.3%)

Compiler: Compiled 116 to 86 computations (25.9% saved)

analyze0.0ms (0%)

sample772.0ms (37.4%)

preprocess353.0ms (17.1%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize40.0ms (1.9%)

series3.0ms (0.2%)

rewrite56.0ms (2.7%)

simplify59.0ms (2.8%)

eval10.0ms (0.5%)

prune7.0ms (0.3%)

localize54.0ms (2.6%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes16.0ms (0.8%)

regimes26.0ms (1.3%)

regimes6.0ms (0.3%)

bsearch37.0ms (1.8%)

simplify8.0ms (0.4%)

soundness566.0ms (27.4%)

end0.0ms (0%)

preprocess47.0ms (2.3%)

Profiling