Metrics for Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

analyze1.0ms (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 12 to 8 computations (33.3% saved)

sample969.0ms (45%)

Results

742.0ms	5874×	body	256	valid
216.0ms	2382×	body	256	infinite

Bogosity

preprocess82.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2344×	`fma-def`
306×	`unsub-neg`
300×	`associate-r`
254×	`distribute-lft-in`
188×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	103
1	74	95
2	171	95
3	552	95
4	1319	95
5	2494	95
6	2759	95
7	2819	95
8	2819	95

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 2 (-.f64 (.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (neg.f64 x) y)))
(.f64 2 (.f64 x (-.f64 x (neg.f64 y))))
(.f64 2 (.f64 x (+.f64 x y)))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x (neg.f64 y))))
(.f64 2 (.f64 x (-.f64 x (neg.f64 y))))
(.f64 2 (.f64 x (+.f64 x y)))
(.f64 2 (-.f64 (.f64 y y) (*.f64 y x)))
(.f64 2 (.f64 y (-.f64 y x)))
(.f64 (.f64 2 y) (-.f64 y x))
(.f64 (.f64 y -2) (-.f64 x y))
(.f64 (-.f64 x y) (.f64 y -2))

Compiler

Compiled 11 to 7 computations (36.4% saved)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize25.0ms (1.1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 x (-.f64 x y)))

Compiler

Compiled 21 to 8 computations (61.9% saved)

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(.f64 2 (.f64 x (-.f64 x y)))
1.0ms	y	@	0	(.f64 2 (.f64 x (-.f64 x y)))
0.0ms	x	@	0	(.f64 2 (.f64 x (-.f64 x y)))
0.0ms	y	@	inf	(.f64 2 (.f64 x (-.f64 x y)))
0.0ms	x	@	-inf	(.f64 2 (.f64 x (-.f64 x y)))

rewrite59.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1844×	`pow1`
1710×	`add-exp-log`
1708×	`log1p-expm1-u`
1708×	`expm1-log1p-u`
1678×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	173	19
2	2285	19

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(.f64 2 (.f64 x (-.f64 x y)))

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

simplify57.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1178×	`associate-r`
1046×	`associate-l`
976×	`log-prod`
512×	`associate-+r+`
456×	`associate-+l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	999
1	177	935
2	612	743
3	4016	743

Stop Event

1×	node limit

Counts

39 → 28

Calls

Call 1

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

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

eval7.0ms (0.3%)

Compiler: Compiled 312 to 164 computations (47.4% saved)

prune6.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	3	29

Accuracy

100.0%

Counts

29 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 x 2) (-.f64 x y))
▶	55.0%	(.f64 2 (.f64 x x))
▶	59.3%	(.f64 -2 (.f64 y x))
▶	100.0%	(.f64 (.f64 x 2) (-.f64 x y))
▶	55.0%	(.f64 2 (.f64 x x))
▶	59.3%	(.f64 -2 (.f64 y x))

Compiler

Compiled 46 to 32 computations (30.4% saved)

localize52.0ms (2.4%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 x x))
✓	100.0%	(.f64 -2 (.f64 y x))

Compiler

Compiled 40 to 18 computations (55% saved)

series4.0ms (0.2%)

Counts

2 → 12

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(.f64 -2 (.f64 y x))
0.0ms	x	@	inf	(.f64 -2 (.f64 y x))
0.0ms	x	@	0	(.f64 -2 (.f64 y x))
0.0ms	y	@	inf	(.f64 -2 (.f64 y x))
0.0ms	x	@	0	(.f64 2 (.f64 x x))

rewrite120.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1774×	`pow1`
1626×	`add-exp-log`
1626×	`log1p-expm1-u`
1626×	`expm1-log1p-u`
1590×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	202	26
2	2294	26

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(.f64 2 (.f64 x x))

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

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1420×	`exp-sum`
1388×	`log-prod`
970×	`fma-def`
940×	`distribute-rgt-in`
916×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	574
1	160	508
2	612	442
3	2043	442
4	6922	442

Stop Event

1×	node limit

Counts

34 → 27

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

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 -2 (.f64 y x))) 1)
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(pow.f64 (.f64 -2 (.f64 y x)) 1)
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(pow.f64 (cbrt.f64 (.f64 -2 (.f64 y x))) 3)
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(pow.f64 (pow.f64 (.f64 -2 (.f64 y x)) 3) 1/3)
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(pow.f64 (sqrt.f64 (.f64 -2 (.f64 y x))) 2)
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(sqrt.f64 (.f64 4 (pow.f64 (.f64 y x) 2)))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) y) -2))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(cbrt.f64 (pow.f64 (.f64 -2 (.f64 y x)) 3))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(expm1.f64 (log1p.f64 (.f64 -2 (.f64 y x))))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(exp.f64 (log.f64 (.f64 -2 (.f64 y x))))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(log1p.f64 (expm1.f64 (.f64 -2 (.f64 y x))))
(+.f64 1 (-.f64 (.f64 (.f64 -2 y) x) 1))
(+.f64 (.f64 x (.f64 -2 y)) 0)
(.f64 x (.f64 -2 y))
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(.f64 2 (.f64 x x))
(pow.f64 (.f64 2 (.f64 x x)) 1)
(.f64 2 (.f64 x x))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(.f64 2 (.f64 x x))
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 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 2) (*.f64 x x)))
(.f64 2 (.f64 x x))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(.f64 2 (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))

eval5.0ms (0.2%)

Compiler: Compiled 199 to 130 computations (34.7% saved)

prune35.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	27	3	30

Accuracy

100.0%

Counts

30 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 x 2) (-.f64 x y))
▶	59.3%	(.f64 x (.f64 -2 y))
✓	55.0%	(.f64 2 (.f64 x x))
✓	100.0%	(.f64 (.f64 x 2) (-.f64 x y))
▶	59.3%	(.f64 x (.f64 -2 y))
✓	55.0%	(.f64 2 (.f64 x x))

Compiler

Compiled 46 to 32 computations (30.4% saved)

localize22.0ms (1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
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 2) (-.f64 x y))
✓	59.3%	(.f64 x (.f64 -2 y))
✓	55.0%	(.f64 2 (.f64 x x))

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes73.0ms (3.4%)

Counts

6 → 1

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(.f64 2 (.f64 x x))
(.f64 x (.f64 -2 y))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

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

Calls

4 calls:

39.0ms	x
23.0ms	(-.f64 (.f64 x x) (.f64 x y))
5.0ms	y
4.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Results

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

Compiler

Compiled 66 to 38 computations (42.4% saved)

regimes10.0ms (0.5%)

Counts

4 → 1

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(.f64 2 (.f64 x x))
(.f64 x (.f64 -2 y))
(.f64 2 (.f64 x (-.f64 x y)))

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

Calls

2 calls:

5.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 30 to 19 computations (36.7% saved)

regimes48.0ms (2.2%)

Counts

3 → 5

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(.f64 2 (.f64 x x))
(.f64 x (.f64 -2 y))

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

Calls

2 calls:

28.0ms	x
20.0ms	y

Results

Accuracy	Segments	Branch
83.2%	5	`x`
87.4%	5	`y`

Compiler

Compiled 23 to 15 computations (34.8% saved)

regimes7.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))

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

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
59.3%	1	`x`
59.3%	1	`y`

Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch52.0ms (2.4%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
17.0ms	6.395711369898251e+30	8.112945753077757e+42
16.0ms	-2.0360513060351292e-10	-3.506201415728152e-16
8.0ms	-8.752305957657846e+59	-3.653476555720806e+59
10.0ms	-2.6240207809883543e+103	-1.937632944829643e+102

Results

36.0ms	366×	body	256	valid
10.0ms	114×	body	256	infinite

Compiler

Compiled 496 to 371 computations (25.2% saved)

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative`
8×	`not-or`
6×	`not-not`
6×	`if-if-or-not`
6×	`if-not`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	146
1	45	140
2	53	134
3	61	130
4	66	130
5	70	130
6	71	130
7	72	130

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 x 2) (-.f64 x y))
(.f64 2 (.f64 x (-.f64 x y)))
(if (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (.f64 -2 (.f64 y x)) (if (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (.f64 2 (.f64 x x)) (if (<=.f64 y -290142196707511/38685626227668133590597632) (.f64 -2 (.f64 y x)) (if (<=.f64 y 7000000000000000195487369212723200) (.f64 2 (.f64 x x)) (.f64 -2 (.f64 y x))))))
(.f64 -2 (.f64 y x))

Outputs
(.f64 (.f64 x 2) (-.f64 x y))
(.f64 2 (.f64 x (-.f64 x y)))
(if (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (.f64 -2 (.f64 y x)) (if (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (.f64 2 (.f64 x x)) (if (<=.f64 y -290142196707511/38685626227668133590597632) (.f64 -2 (.f64 y x)) (if (<=.f64 y 7000000000000000195487369212723200) (.f64 2 (.f64 x x)) (.f64 -2 (.f64 y x))))))
(if (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (.f64 -2 (.f64 x y)) (if (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (.f64 2 (.f64 x x)) (if (or (<=.f64 y -290142196707511/38685626227668133590597632) (not (<=.f64 y 7000000000000000195487369212723200))) (.f64 -2 (.f64 x y)) (.f64 2 (.f64 x x)))))
(if (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (.f64 -2 (.f64 x y)) (if (or (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (not (or (<=.f64 y -290142196707511/38685626227668133590597632) (not (<=.f64 y 7000000000000000195487369212723200))))) (.f64 2 (.f64 x x)) (.f64 -2 (.f64 x y))))
(if (or (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (not (or (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (not (or (<=.f64 y -290142196707511/38685626227668133590597632) (not (<=.f64 y 7000000000000000195487369212723200))))))) (.f64 -2 (.f64 x y)) (.f64 2 (.f64 x x)))
(if (or (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (not (or (<=.f64 y -780000000000000042588707862310427877083086351936430199013376) (and (not (<=.f64 y -290142196707511/38685626227668133590597632)) (<=.f64 y 7000000000000000195487369212723200))))) (.f64 -2 (.f64 x y)) (.f64 2 (.f64 x x)))
(if (or (<=.f64 y -1999999999999999954099026530490673256893685439848300012259991949463986904361579822606522588963023093760) (and (not (<=.f64 y -780000000000000042588707862310427877083086351936430199013376)) (or (<=.f64 y -290142196707511/38685626227668133590597632) (not (<=.f64 y 7000000000000000195487369212723200))))) (.f64 -2 (.f64 x y)) (.f64 2 (.f64 x x)))
(.f64 -2 (.f64 y x))
(.f64 -2 (.f64 x y))

Compiler

Compiled 55 to 39 computations (29.1% saved)

soundness308.0ms (14.3%)

Rules

2344×	`fma-def`
1178×	`associate-r`
1178×	`associate-r`
1046×	`associate-l`
1046×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	103
1	74	95
2	171	95
3	552	95
4	1319	95
5	2494	95
6	2759	95
7	2819	95
8	2819	95
0	63	999
1	177	935
2	612	743
3	4016	743
0	63	999
1	177	935
2	612	743
3	4016	743

Stop Event

1×	node limit
1×	node limit
1×	saturated

Compiler

Compiled 124 to 76 computations (38.7% saved)

end0.0ms (0%)

preprocess103.0ms (4.8%)

Compiler: Compiled 138 to 88 computations (36.2% saved)

analyze1.0ms (0%)

sample969.0ms (45%)

preprocess82.0ms (3.8%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize25.0ms (1.1%)

series7.0ms (0.3%)

rewrite59.0ms (2.7%)

simplify57.0ms (2.7%)

eval7.0ms (0.3%)

prune6.0ms (0.3%)

localize52.0ms (2.4%)

series4.0ms (0.2%)

rewrite120.0ms (5.6%)

simplify72.0ms (3.3%)

eval5.0ms (0.2%)

prune35.0ms (1.6%)

localize22.0ms (1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes73.0ms (3.4%)

regimes10.0ms (0.5%)

regimes48.0ms (2.2%)

regimes7.0ms (0.3%)

bsearch52.0ms (2.4%)

simplify28.0ms (1.3%)

soundness308.0ms (14.3%)

end0.0ms (0%)

preprocess103.0ms (4.8%)

Profiling