Details

analyze70.0ms (5.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
48%	37.5%	40.6%	0.1%	21.9%	0%	0%	7
57.1%	43.7%	32.8%	0.1%	23.4%	0%	0%	8
71.4%	54.6%	21.9%	0.1%	23.4%	0%	0%	9
77.3%	58.5%	17.2%	0.1%	24.2%	0%	0%	10
85.1%	64.4%	11.3%	0.1%	24.2%	0%	0%	11
88.3%	66.5%	8.8%	0.1%	24.6%	0%	0%	12

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample846.0ms (65.4%)

Results

799.0ms	8256×	body	256	valid
32.0ms	37×	body	256	infinite

Bogosity

preprocess17.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

204×	`fma-def`
64×	`associate-+l-`
58×	`associate--r+`
56×	`associate-+r+`
52×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	19	26
2	35	26
3	58	26
4	85	26
5	182	26
6	320	26
7	392	26
8	478	26
9	488	26
10	490	26
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify22.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

112×	`fma-def`
58×	`associate--r+`
52×	`associate-+l-`
50×	`+-commutative`
40×	`associate--l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	12	13
2	21	13
3	33	13
4	48	13
5	85	13
6	141	13
7	186	13
8	259	13
9	351	13
10	384	13
11	388	13

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(-.f64 x (*.f64 y y))

Compiler

Compiled 7 to 4 computations (42.9% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y y))

Compiler

Compiled 12 to 4 computations (66.7% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

1442×	`add-sqr-sqrt`
1422×	`*-un-lft-identity`
1332×	`add-cube-cbrt`
1320×	`add-cbrt-cube`
1310×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	133	13
2	1846	13

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (.f64 y (neg.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (.f64 y y)) (fma.f64 (neg.f64 y) y (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (.f64 y y)) (fma.f64 (.f64 y (neg.f64 y)) 1 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (.f64 y y)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (neg.f64 y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 x (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 x (.f64 y y))) (sqrt.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 x (.f64 y y))) (pow.f64 (cbrt.f64 (-.f64 x (.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y y))) 2) (cbrt.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (pow.f64 y 4)) (/.f64 1 (+.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 x) y) (-.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (.f64 y y)) (-.f64 (.f64 x x) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y)))) (-.f64 (pow.f64 x 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (pow.f64 y 4)) (+.f64 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (.f64 (.f64 y (neg.f64 y)) (.f64 y (neg.f64 y)))) (-.f64 x (.f64 y (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (neg.f64 y)) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (neg.f64 y)) (.f64 y (neg.f64 y))) (.f64 x (.f64 y (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 y 4))) (neg.f64 (+.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6))) (neg.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 x (.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 x (.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 x (.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 x (.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 x (.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (-.f64 x (.f64 y y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 y (neg.f64 y)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (*.f64 y (neg.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (*.f64 y (neg.f64 y)) 1 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (neg.f64 y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 x (*.f64 y y))) (sqrt.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 2) (cbrt.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 y 4)) (/.f64 1 (+.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 x) y) (-.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (*.f64 y y)) (-.f64 (*.f64 x x) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y)))) (-.f64 (pow.f64 x 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 y 4)) (+.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y (neg.f64 y)) (*.f64 y (neg.f64 y)))) (-.f64 x (*.f64 y (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (neg.f64 y)) 3)) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 y (neg.f64 y)) (*.f64 y (neg.f64 y))) (*.f64 x (*.f64 y (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 y 4))) (neg.f64 (+.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6))) (neg.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 x (*.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 x (*.f64 y y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 y (neg.f64 y)))))))

simplify58.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1026×	`associate-+r+`
762×	`associate-+l+`
714×	`*-commutative`
562×	`fma-def`
554×	`distribute-lft-neg-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1032
1	270	982
2	1181	954
3	4027	952

Stop Event

1×	node limit

Counts

60 → 48

Calls

Call 1

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

Outputs
(*.f64 -1 (pow.f64 y 2))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(*.f64 -1 (pow.f64 y 2))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(*.f64 -1 (pow.f64 y 2))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 x (*.f64 y (neg.f64 y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 x (.f64 (.f64 y (neg.f64 y)) 1))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (-.f64 x (.f64 y y)) (fma.f64 (neg.f64 y) y (.f64 y y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (-.f64 x (.f64 y y)) (fma.f64 (.f64 y (neg.f64 y)) 1 (*.f64 y y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(+.f64 (-.f64 x (.f64 y y)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (.f64 y y)))
(+.f64 (fma.f64 y (neg.f64 y) x) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (*.f64 y y)))
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (+.f64 x 0))
(+.f64 x (*.f64 (pow.f64 (cbrt.f64 y) 2) (neg.f64 (cbrt.f64 (pow.f64 y 4)))))
(+.f64 (*.f64 y (neg.f64 y)) x)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (-.f64 x (.f64 y y)) 1)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 1 (-.f64 x (.f64 y y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (sqrt.f64 (-.f64 x (.f64 y y))) (sqrt.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (cbrt.f64 (-.f64 x (.f64 y y))) (pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 2))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (pow.f64 (cbrt.f64 (-.f64 x (.f64 y y))) 2) (cbrt.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (-.f64 (.f64 x x) (pow.f64 y 4)) (/.f64 1 (+.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (*.f64 y y))))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 (*.f64 x y) y)))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (.f64 (.f64 y y) (fma.f64 y y x))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (*.f64 x (fma.f64 y y x))))
(*.f64 (+.f64 (sqrt.f64 x) y) (-.f64 (sqrt.f64 x) y))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(/.f64 1 (/.f64 (+.f64 x (.f64 y y)) (-.f64 (.f64 x x) (pow.f64 y 4))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(/.f64 1 (/.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y)))) (-.f64 (pow.f64 x 3) (pow.f64 y 6))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 (*.f64 x y) y)))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (.f64 (.f64 y y) (fma.f64 y y x))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (*.f64 x (fma.f64 y y x))))
(/.f64 (-.f64 (.f64 x x) (pow.f64 y 4)) (+.f64 x (.f64 y y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y)))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 (*.f64 x y) y)))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (.f64 (.f64 y y) (fma.f64 y y x))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (*.f64 x (fma.f64 y y x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y (neg.f64 y)) (.f64 y (neg.f64 y)))) (-.f64 x (*.f64 y (neg.f64 y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (neg.f64 y)) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (neg.f64 y)) (.f64 y (neg.f64 y))) (.f64 x (*.f64 y (neg.f64 y))))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 (*.f64 x y) y)))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (.f64 (.f64 y y) (fma.f64 y y x))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (*.f64 x (fma.f64 y y x))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 y 4))) (neg.f64 (+.f64 x (.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6))) (neg.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 x (.f64 y y))))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (.f64 (*.f64 x y) y)))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (.f64 (.f64 y y) (fma.f64 y y x))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (*.f64 x (fma.f64 y y x))))
(pow.f64 (-.f64 x (*.f64 y y)) 1)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y y))) 2)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 3)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(pow.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3) 1/3)
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(sqrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 2))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(log.f64 (exp.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(cbrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(expm1.f64 (log1p.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(exp.f64 (log.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(exp.f64 (.f64 (log.f64 (-.f64 x (.f64 y y))) 1))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(log1p.f64 (expm1.f64 (-.f64 x (*.f64 y y))))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(fma.f64 1 x (*.f64 y (neg.f64 y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 y (neg.f64 y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 y (neg.f64 y)))
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))

eval9.0ms (0.7%)

Compiler: Compiled 572 to 228 computations (60.1% saved)

prune8.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(fma.f64 y (neg.f64 y) x)
✓	0.0b	(-.f64 x (*.f64 y y))
▶	42.1b	(*.f64 y (neg.f64 y))
	20.6b	x

Compiler

Compiled 23 to 14 computations (39.1% saved)

localize4.0ms (0.3%)

Compiler: Compiled 9 to 4 computations (55.6% saved)

localize5.0ms (0.3%)

Compiler: Compiled 11 to 4 computations (63.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 y (neg.f64 y) x)
✓	0.0b	(-.f64 x (*.f64 y y))
✓	42.1b	(*.f64 y (neg.f64 y))
	20.6b	x

Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

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

prune3.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 y (neg.f64 y) x)
✓	0.0b	(-.f64 x (*.f64 y y))
✓	42.1b	(*.f64 y (neg.f64 y))
	20.6b	x

Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 y (neg.f64 y) x)
✓	0.0b	(-.f64 x (*.f64 y y))
✓	42.1b	(*.f64 y (neg.f64 y))
	20.6b	x

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes15.0ms (1.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(fma.f64 y (neg.f64 y) x)

Calls

4 calls:

4.0ms	y
3.0ms	(-.f64 x (*.f64 y y))
3.0ms	x
3.0ms	(*.f64 y y)

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`(-.f64 x (*.f64 y y))`
0b	1	`(*.f64 y y)`

Compiler

Compiled 35 to 18 computations (48.6% saved)

regimes14.0ms (1.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(-.f64 x (*.f64 y y))
3.0ms	x
3.0ms	y
2.0ms	(*.f64 y y)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(-.f64 x (*.f64 y y))`
0.0b	1	`(*.f64 y y)`

Compiler

Compiled 30 to 17 computations (43.3% saved)

regimes25.0ms (1.9%)

Accuracy

Total -52.5b remaining (-561.7%)

Threshold costs -52.5b (-561.7%)

Counts

2 → 3

Calls

Call 1

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

Outputs
(*.f64 y (neg.f64 y))
x
(*.f64 y (neg.f64 y))

Calls

2 calls:

14.0ms	x
9.0ms	y

Results

Error	Segments	Branch
15.7b	5	`x`
9.3b	3	`y`

Compiler

Compiled 13 to 8 computations (38.5% saved)

bsearch22.0ms (1.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
13.0ms	9.479263136928276e-16	2.147695297469917e-11
8.0ms	-2.521190117703813e-30	-3.5175217459609834e-31

Results

19.0ms

224×

body

256

valid

Compiler

Compiled 166 to 120 computations (27.7% saved)

simplify6.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
6×	`*-commutative`
4×	`neg-mul-1`
4×	`cancel-sign-sub-inv`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	32	64
2	37	64
3	40	64
4	41	64

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(if (<=.f64 y -8278036617694567/5708990770823839524233143877797980545530986496) (.f64 y (neg.f64 y)) (if (<=.f64 y 4951760157141521/4951760157141521099596496896) x (.f64 y (neg.f64 y))))
x

Outputs
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(if (<=.f64 y -8278036617694567/5708990770823839524233143877797980545530986496) (.f64 y (neg.f64 y)) (if (<=.f64 y 4951760157141521/4951760157141521099596496896) x (.f64 y (neg.f64 y))))
(if (or (<=.f64 y -8278036617694567/5708990770823839524233143877797980545530986496) (not (<=.f64 y 4951760157141521/4951760157141521099596496896))) (*.f64 y (neg.f64 y)) x)
x

Compiler

Compiled 33 to 21 computations (36.4% saved)

soundness86.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1026×	`associate-+r+`
762×	`associate-+l+`
714×	`*-commutative`
562×	`fma-def`
554×	`distribute-lft-neg-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1032
1	270	982
2	1181	954
3	4027	952

Stop Event

1×	node limit

Compiler

Compiled 32 to 18 computations (43.8% saved)

end24.0ms (1.8%)

Compiler: Compiled 27 to 14 computations (48.1% saved)

Iter	Nodes	Cost
0	8	26
1	19	26
2	35	26
3	58	26
4	85	26
5	182	26
6	320	26
7	392	26
8	478	26
9	488	26
10	490	26
0	2	2

Iter	Nodes	Cost
0	6	13
1	12	13
2	21	13
3	33	13
4	48	13
5	85	13
6	141	13
7	186	13
8	259	13
9	351	13
10	384	13
11	388	13

Iter	Nodes	Cost
0	8	26
1	19	26
2	35	26
3	58	26
4	85	26
5	182	26
6	320	26
7	392	26
8	478	26
9	488	26
10	490	26
0	2	2

Iter	Nodes	Cost
0	6	13
1	12	13
2	21	13
3	33	13
4	48	13
5	85	13
6	141	13
7	186	13
8	259	13
9	351	13
10	384	13
11	388	13

Details

analyze70.0ms (5.4%)

sample846.0ms (65.4%)

preprocess17.0ms (1.3%)

simplify22.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.3%)

series1.0ms (0.1%)

rewrite52.0ms (4%)

simplify58.0ms (4.5%)

eval9.0ms (0.7%)

prune8.0ms (0.6%)

localize4.0ms (0.3%)

localize5.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes15.0ms (1.1%)

regimes14.0ms (1.1%)

regimes25.0ms (1.9%)

bsearch22.0ms (1.7%)

simplify6.0ms (0.5%)

soundness86.0ms (6.6%)

end24.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	8	26
1	19	26
2	35	26
3	58	26
4	85	26
5	182	26
6	320	26
7	392	26
8	478	26
9	488	26
10	490	26
0	2	2

Iter	Nodes	Cost
0	6	13
1	12	13
2	21	13
3	33	13
4	48	13
5	85	13
6	141	13
7	186	13
8	259	13
9	351	13
10	384	13
11	388	13