Metrics for Linear.Matrix:fromQuaternion from linear-1.19.1.3, 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 12 to 8 computations (33.3% saved)

sample1.0s (51.3%)

Results

779.0ms	5894×	body	256	valid
211.0ms	2362×	body	256	infinite

Bogosity

preprocess195.0ms (10%)

Algorithm

1×	egg-herbie

Rules

1072×	`fma-neg`
554×	`fma-def`
344×	`unsub-neg`
318×	`associate-r`
296×	`distribute-lft-in`

Problems

245×	No Errors
11×	`(-.f64 (.f64 x x) (.f64 x y))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	212
1	91	196
2	210	196
3	719	196
4	1657	196
5	2105	196
6	2475	196
7	2594	196
8	2594	196

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

Compiler

Compiled 39 to 16 computations (59% 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 (1.3%)

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)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite176.0ms (9%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`unpow-prod-down`
718×	`prod-diff`
650×	`log-prod`
612×	`log1p-expm1-u`
612×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	120	28
2	1614	28

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

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

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

simplify53.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1346×	`associate-r`
1208×	`associate-l`
1032×	`log-prod`
574×	`distribute-lft-in`
548×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1915
1	226	1880
2	703	1491
3	5233	1467

Stop Event

1×	node limit

Counts

52 → 42

Calls

Call 1

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

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

eval11.0ms (0.5%)

Compiler: Compiled 517 to 301 computations (41.8% saved)

prune7.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Accuracy

100.0%

Counts

43 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 x (.f64 2 (-.f64 x y)))
▶	49.4%	(.f64 x (.f64 -2 y))
▶	49.4%	(.f64 -2 (.f64 x y))
▶	100.0%	(.f64 x (.f64 2 (-.f64 x y)))
▶	49.4%	(.f64 x (.f64 -2 y))
▶	49.4%	(.f64 -2 (.f64 x y))

Compiler

Compiled 46 to 32 computations (30.4% saved)

localize68.0ms (3.5%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 43 to 20 computations (53.5% saved)

series3.0ms (0.2%)

Counts

1 → 0

Calls

6 calls:

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

rewrite47.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`unpow-prod-down`
472×	`log-prod`
462×	`cbrt-prod`
364×	`log1p-expm1-u`
364×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	88	19
2	1001	19

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

simplify53.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1872×	`log-prod`
770×	`associate-r`
708×	`exp-sum`
684×	`associate-l`
636×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	541
1	153	541
2	470	541
3	3067	541
4	6447	541

Stop Event

1×	node limit

Counts

21 → 22

Calls

Call 1

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

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

eval5.0ms (0.3%)

Compiler: Compiled 215 to 159 computations (26% saved)

prune5.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	22	3	25

Accuracy

100.0%

Counts

25 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 x (.f64 2 (-.f64 x y)))
✓	49.4%	(.f64 x (.f64 -2 y))
✓	49.4%	(.f64 -2 (.f64 x y))

Compiler

Compiled 58 to 35 computations (39.7% saved)

regimes28.0ms (1.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

12.0ms	(-.f64 (.f64 x x) (.f64 x y))
6.0ms	y
4.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
4.0ms	x

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 61 to 35 computations (42.6% saved)

regimes8.0ms (0.4%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

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

Compiler

Compiled 25 to 16 computations (36% saved)

regimes8.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
49.4%	1	`x`
49.4%	1	`y`

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative`
4×	`sub-neg`
4×	`+-commutative`
2×	`neg-mul-1`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	75
1	25	75
2	30	75
3	32	75
4	33	75

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 25 to 17 computations (32% saved)

soundness211.0ms (10.8%)

Rules

1346×	`associate-r`
1208×	`associate-l`
1072×	`fma-neg`
1032×	`log-prod`
574×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	212
1	91	196
2	210	196
3	719	196
4	1657	196
5	2105	196
6	2475	196
7	2594	196
8	2594	196
0	93	1915
1	226	1880
2	703	1491
3	5233	1467

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 119 to 75 computations (37% saved)

end0.0ms (0%)

preprocess40.0ms (2.1%)

Compiler: Compiled 82 to 50 computations (39% saved)

analyze0.0ms (0%)

sample1.0s (51.3%)

preprocess195.0ms (10%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize25.0ms (1.3%)

series3.0ms (0.2%)

rewrite176.0ms (9%)

simplify53.0ms (2.7%)

eval11.0ms (0.5%)

prune7.0ms (0.4%)

localize68.0ms (3.5%)

series3.0ms (0.2%)

rewrite47.0ms (2.4%)

simplify53.0ms (2.7%)

eval5.0ms (0.3%)

prune5.0ms (0.3%)

regimes28.0ms (1.4%)

regimes8.0ms (0.4%)

regimes8.0ms (0.4%)

simplify3.0ms (0.2%)

soundness211.0ms (10.8%)

end0.0ms (0%)

preprocess40.0ms (2.1%)

Profiling