Metrics for System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

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 10 to 7 computations (30% saved)

sample687.0ms (39.7%)

Results

510.0ms	6221×	body	256	valid
165.0ms	2034×	body	256	infinite
0.0ms	1×	body	1024	valid

Bogosity

preprocess51.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def`
142×	`unsub-neg`
130×	`associate-r`
98×	`distribute-lft-in`
78×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	99
1	42	91
2	100	91
3	291	91
4	649	91
5	1053	91
6	1203	91
7	1214	91

Stop Event

1×

saturated

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize24.0ms (1.4%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 21 to 8 computations (61.9% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite64.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1408×	`pow1`
1308×	`add-exp-log`
1308×	`log1p-expm1-u`
1308×	`expm1-log1p-u`
1280×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	132	13
2	1799	13

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x x) (neg.f64 y))
(+.f64 (.f64 x x) (.f64 (neg.f64 y) 1))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 y) 1 y))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y))
(+.f64 (neg.f64 y) (*.f64 x x))
(.f64 (-.f64 (.f64 x x) y) 1)
(.f64 1 (-.f64 (.f64 x x) y))
(.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 2))
(.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) 2) (cbrt.f64 (-.f64 (*.f64 x x) y)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) y)) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (fma.f64 x x y)))
(*.f64 (+.f64 x (sqrt.f64 y)) (-.f64 x (sqrt.f64 y)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))) (-.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 1 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x 4) (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x y))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (fma.f64 x x y)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) (.f64 (*.f64 x x) (neg.f64 y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (.f64 x x) (neg.f64 y)))
(pow.f64 (-.f64 (*.f64 x x) y) 1)
(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 3)
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) 2)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 2))
(log.f64 (exp.f64 (-.f64 (*.f64 x x) y)))
(cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3))
(expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) y)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) y)))
(log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) y)))
(fma.f64 x x (neg.f64 y))
(fma.f64 1 (*.f64 x x) (neg.f64 y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (neg.f64 y))

simplify66.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1348×	`div-sub`
1026×	`fma-neg`
790×	`fma-def`
750×	`associate-r`
680×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	101	965
1	249	915
2	892	915
3	4610	915

Stop Event

1×	node limit

Counts

59 → 43

Calls

Call 1

Inputs
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (*.f64 x x) (neg.f64 y))
(+.f64 (.f64 x x) (.f64 (neg.f64 y) 1))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 y) 1 y))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y))
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y))
(+.f64 (neg.f64 y) (*.f64 x x))
(.f64 (-.f64 (.f64 x x) y) 1)
(.f64 1 (-.f64 (.f64 x x) y))
(.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 2))
(.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) 2) (cbrt.f64 (-.f64 (*.f64 x x) y)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) y)) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (fma.f64 x x y)))
(*.f64 (+.f64 x (sqrt.f64 y)) (-.f64 x (sqrt.f64 y)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))) (-.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 1 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x 4) (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x y))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (fma.f64 x x y)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) (.f64 (*.f64 x x) (neg.f64 y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (.f64 x x) (neg.f64 y)))
(pow.f64 (-.f64 (*.f64 x x) y) 1)
(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 3)
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) 2)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 2))
(log.f64 (exp.f64 (-.f64 (*.f64 x x) y)))
(cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3))
(expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) y)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) y)))
(log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) y)))
(fma.f64 x x (neg.f64 y))
(fma.f64 1 (*.f64 x x) (neg.f64 y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (neg.f64 y))

Outputs
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (*.f64 x x) (neg.f64 y))
(-.f64 (*.f64 x x) y)
(+.f64 (.f64 x x) (.f64 (neg.f64 y) 1))
(-.f64 (*.f64 x x) y)
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 y) 1 y))
(-.f64 (*.f64 x x) y)
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y))
(-.f64 (*.f64 x x) y)
(+.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y))
(-.f64 (*.f64 x x) y)
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(.f64 (-.f64 (.f64 x x) y) 1)
(-.f64 (*.f64 x x) y)
(.f64 1 (-.f64 (.f64 x x) y))
(-.f64 (*.f64 x x) y)
(.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 2))
(-.f64 (*.f64 x x) y)
(.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 x x) y)) 2) (cbrt.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) y)) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (fma.f64 x x y) (pow.f64 x 4)))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (fma.f64 x x y)))
(-.f64 (*.f64 x x) y)
(*.f64 (+.f64 x (sqrt.f64 y)) (-.f64 x (sqrt.f64 y)))
(-.f64 (*.f64 x x) y)
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))) (-.f64 (pow.f64 x 6) (pow.f64 y 3))))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (fma.f64 x x y) (pow.f64 x 4)))
(/.f64 1 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x 4) (*.f64 y y))))
(-.f64 (*.f64 x x) y)
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (fma.f64 x x y) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x y))
(-.f64 (*.f64 x x) y)
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y)))))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (fma.f64 x x y) (pow.f64 x 4)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (fma.f64 x x y)))
(-.f64 (*.f64 x x) y)
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) (.f64 (*.f64 x x) (neg.f64 y)))))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (fma.f64 x x y) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (.f64 x x) (neg.f64 y)))
(-.f64 (*.f64 x x) y)
(pow.f64 (-.f64 (*.f64 x x) y) 1)
(-.f64 (*.f64 x x) y)
(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 3)
(-.f64 (*.f64 x x) y)
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3) 1/3)
(-.f64 (*.f64 x x) y)
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) 2)
(-.f64 (*.f64 x x) y)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 2))
(-.f64 (*.f64 x x) y)
(log.f64 (exp.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3))
(-.f64 (*.f64 x x) y)
(expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(exp.f64 (log.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) y)))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(-.f64 (*.f64 x x) y)
(fma.f64 1 (*.f64 x x) (neg.f64 y))
(-.f64 (*.f64 x x) y)
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (neg.f64 y))
(-.f64 (.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x))) y)

eval9.0ms (0.5%)

Compiler: Compiled 536 to 264 computations (50.7% saved)

prune9.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Accuracy

100.0%

Counts

44 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
✓	100.0%	(.f64 1/2 (-.f64 (.f64 x x) y))
▶	52.4%	(.f64 1/2 (.f64 x x))
▶	49.6%	(*.f64 1/2 (neg.f64 y))
▶	100.0%	(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
✓	100.0%	(.f64 1/2 (-.f64 (.f64 x x) y))
▶	52.4%	(.f64 1/2 (.f64 x x))
▶	49.6%	(*.f64 1/2 (neg.f64 y))

Compiler

Compiled 62 to 44 computations (29% saved)

localize41.0ms (2.4%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 1/2 (.f64 x x))

Compiler

Compiled 38 to 15 computations (60.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 1/2 (.f64 x x))
0.0ms	x	@	0	(.f64 1/2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 1/2 (.f64 x x))

rewrite51.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1058×	`pow1`
1024×	`add-sqr-sqrt`
976×	`add-exp-log`
976×	`log1p-expm1-u`
976×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1383	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x x))

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

simplify107.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

2120×	`log-prod`
1106×	`distribute-rgt-in`
1092×	`distribute-lft-in`
768×	`associate-r`
688×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	90	299
2	319	299
3	2131	299
4	7005	299

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

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

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

eval3.0ms (0.1%)

Compiler: Compiled 93 to 61 computations (34.4% saved)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
✓	100.0%	(.f64 1/2 (-.f64 (.f64 x x) y))
✓	52.4%	(.f64 1/2 (.f64 x x))
✓	49.6%	(*.f64 1/2 (neg.f64 y))

Compiler

Compiled 56 to 36 computations (35.7% saved)

regimes21.0ms (1.2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))

Calls

5 calls:

5.0ms	(.f64 1/2 (-.f64 (.f64 x x) y))
4.0ms	y
4.0ms	x
4.0ms	(-.f64 (*.f64 x x) y)
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 52 to 31 computations (40.4% saved)

regimes44.0ms (2.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(.f64 1/2 (-.f64 (.f64 x x) y))

Calls

5 calls:

29.0ms	y
4.0ms	x
4.0ms	(.f64 1/2 (-.f64 (.f64 x x) y))
4.0ms	(-.f64 (*.f64 x x) y)
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 45 to 28 computations (37.8% saved)

regimes153.0ms (8.8%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

141.0ms	y
6.0ms	x
5.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
89.8%	2	`x`
62.6%	3	`y`
89.8%	2	`(*.f64 x x)`

Compiler

Compiled 22 to 15 computations (31.8% saved)

regimes6.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 1/2 (neg.f64 y))

Outputs
(*.f64 1/2 (neg.f64 y))

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
49.6%	1	`y`
49.6%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch51.0ms (3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
51.0ms	1.4047026711127849e-67	1.6703466390676721e-59

Results

49.0ms

144×

body

256

valid

Compiler

Compiled 131 to 109 computations (16.8% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative`
8×	`sub-neg`
8×	`+-commutative`
6×	`neg-mul-1`
6×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	88
1	32	88
2	41	88
3	47	88
4	50	88
5	51	88

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
(.f64 1/2 (-.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) 7463162001623895/452312848583266388373324160190187140051835877600158453279131187530910662656) (.f64 1/2 (neg.f64 y)) (.f64 1/2 (.f64 x x)))
(*.f64 1/2 (neg.f64 y))

Outputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
(.f64 1/2 (-.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) 7463162001623895/452312848583266388373324160190187140051835877600158453279131187530910662656) (.f64 1/2 (neg.f64 y)) (.f64 1/2 (.f64 x x)))
(*.f64 1/2 (neg.f64 y))

Compiler

Compiled 41 to 28 computations (31.7% saved)

soundness285.0ms (16.5%)

Rules

1408×	`pow1`
1348×	`div-sub`
1348×	`div-sub`
1308×	`add-exp-log`
1308×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	132	13
2	1799	13
0	101	965
1	249	915
2	892	915
3	4610	915
0	101	965
1	249	915
2	892	915
3	4610	915

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 39 to 28 computations (28.2% saved)

end0.0ms (0%)

preprocess44.0ms (2.5%)

Remove: (abs x)
Compiler: Compiled 106 to 62 computations (41.5% saved)

analyze0.0ms (0%)

sample687.0ms (39.7%)

preprocess51.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize24.0ms (1.4%)

series1.0ms (0.1%)

rewrite64.0ms (3.7%)

simplify66.0ms (3.8%)

eval9.0ms (0.5%)

prune9.0ms (0.5%)

localize41.0ms (2.4%)

series1.0ms (0%)

rewrite51.0ms (3%)

simplify107.0ms (6.2%)

eval3.0ms (0.1%)

prune4.0ms (0.2%)

regimes21.0ms (1.2%)

regimes44.0ms (2.5%)

regimes153.0ms (8.8%)

regimes6.0ms (0.3%)

bsearch51.0ms (3%)

simplify9.0ms (0.5%)

soundness285.0ms (16.5%)

end0.0ms (0%)

preprocess44.0ms (2.5%)

Profiling