Details

analyze347.0ms (7.5%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	7
18.8%	18.7%	81.1%	0.1%	0%	0%	0%	8
25.6%	25%	72.5%	0.1%	2.3%	0%	0%	9
38.6%	37.4%	59.7%	0.1%	2.7%	0%	0%	10
46.4%	44.5%	51.3%	0.1%	4.1%	0%	0%	11
53.7%	50.3%	43.4%	0.1%	6.1%	0%	0%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.0s (22%)

Results

945.0ms	8255×	body	256	valid
66.0ms	632×	body	256	infinite
0.0ms	1×	body	1024	valid

Bogosity

preprocess11.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

50×	`+-commutative`
44×	`fma-def`
16×	`associate-+l+`
8×	`associate-+r+`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	100
1	41	84
2	79	84
3	93	84
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 y 2) (*.f64 x y)) z)
(+.f64 (+.f64 (/.f64 z 2) (*.f64 y z)) x)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 z x)) y)

Outputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
(+.f64 (/.f64 x 2) (fma.f64 x y z))
(+.f64 (+.f64 (/.f64 y 2) (*.f64 x y)) z)
(+.f64 z (+.f64 (*.f64 x y) (/.f64 y 2)))
(+.f64 z (fma.f64 x y (/.f64 y 2)))
(+.f64 (+.f64 (/.f64 z 2) (*.f64 y z)) x)
(+.f64 x (+.f64 (/.f64 z 2) (*.f64 y z)))
(+.f64 x (fma.f64 y z (/.f64 z 2)))
(+.f64 (+.f64 (/.f64 x 2) (*.f64 z x)) y)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x z) y))
(+.f64 (/.f64 x 2) (fma.f64 x z y))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`fma-def`
12×	`+-commutative`
4×	`associate-+l+`
2×	`associate-+r+`
2×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	15	21
2	26	21
3	29	21

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)

Outputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
(+.f64 (/.f64 x 2) (fma.f64 x y z))

eval2.0ms (0%)

Compiler: Compiled 29 to 17 computations (41.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))
▶	0.0b	(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))

Compiler

Compiled 23 to 15 computations (34.8% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 27 to 11 computations (59.3% saved)

series2.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1644×	`add-sqr-sqrt`
1628×	`*-un-lft-identity`
1516×	`add-cube-cbrt`
1500×	`add-cbrt-cube`
160×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	150	9
2	2000	9

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

Inputs
(+.f64 (*.f64 x y) z)

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

Outputs

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

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1348×	`associate-r`
1214×	`associate-l`
780×	`associate-+r+`
666×	`distribute-lft-neg-in`
622×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	1159
1	223	1109
2	842	1109
3	4920	1109

Stop Event

1×	node limit

Counts

73 → 45

Calls

Call 1

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

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

localize8.0ms (0.2%)

Compiler: Compiled 22 to 10 computations (54.5% saved)

eval11.0ms (0.2%)

Compiler: Compiled 703 to 327 computations (53.5% saved)

prune7.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	43	4	47

Error

Counts

47 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))
✓	0.0b	(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
▶	30.9b	(+.f64 (/.f64 x 2) (*.f64 y x))
▶	16.0b	(+.f64 (/.f64 x 2) z)

Compiler

Compiled 41 to 28 computations (31.7% saved)

localize6.0ms (0.1%)

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

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x 2) (*.f64 y x))

Compiler

Compiled 19 to 10 computations (47.4% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite59.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1920×	`add-sqr-sqrt`
1890×	`*-un-lft-identity`
1778×	`add-cube-cbrt`
1762×	`add-cbrt-cube`
176×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	178	13
2	2366	13

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

Inputs
(+.f64 (/.f64 x 2) (*.f64 y x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (+.f64 1/2 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 1/4) (.f64 x (-.f64 1/2 y))) (/.f64 (pow.f64 (.f64 x y) 2) (.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (+.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (+.f64 1/2 y))) (sqrt.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) 2) (cbrt.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x (-.f64 1/2 y)) (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))) (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (.f64 x (-.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 (.f64 x y) 2) (-.f64 (.f64 (.f64 x x) 1/4) (.f64 x (.f64 1/2 (.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x y) 2) (.f64 (.f64 x x) 1/4)) (-.f64 (.f64 x y) (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (+.f64 1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (+.f64 1/2 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (+.f64 1/2 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (+.f64 1/2 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (+.f64 1/2 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (+.f64 1/2 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x y (.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y x (.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x 1/2) (.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x y) (.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 1/4)) (cbrt.f64 (.f64 x 1/2)) (.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) (*.f64 x 1/2))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 x (-.f64 1/2 y))) (/.f64 (pow.f64 (*.f64 x y) 2) (*.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 1/2 y))) (sqrt.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (pow.f64 (*.f64 x y) 2)) (/.f64 1 (*.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (*.f64 x y) 3)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x y) (-.f64 (*.f64 x y) (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 1/2 y)) (-.f64 (*.f64 (*.f64 x x) 1/4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x y) (-.f64 (*.f64 x y) (*.f64 x 1/2)))) (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (*.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (pow.f64 (*.f64 x y) 2)) (*.f64 x (-.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x y) (-.f64 (*.f64 x y) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 (*.f64 x y) 2) (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 x (*.f64 1/2 (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (*.f64 (*.f64 x x) 1/4)) (-.f64 (*.f64 x y) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (pow.f64 (*.f64 x y) 2))) (neg.f64 (*.f64 x (-.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (*.f64 x y) 3))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x y) (-.f64 (*.f64 x y) (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 1/2 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 1/2 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x y (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y x (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x y) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/4)) (cbrt.f64 (*.f64 x 1/2)) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) (*.f64 x 1/2))))))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

836×	`distribute-lft-neg-in`
830×	`associate-+r+`
744×	`distribute-rgt-neg-in`
654×	`associate-+l+`
576×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1378
1	286	1328
2	1153	1272
3	4557	1236

Stop Event

1×	node limit

Counts

64 → 56

Calls

Call 1

Inputs
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y)))) 1)
(-.f64 (/.f64 (.f64 (.f64 x x) 1/4) (.f64 x (-.f64 1/2 y))) (/.f64 (pow.f64 (.f64 x y) 2) (*.f64 x (-.f64 1/2 y))))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 y 1/2))
(.f64 (.f64 x (+.f64 1/2 y)) 1)
(.f64 1 (.f64 x (+.f64 1/2 y)))
(.f64 (sqrt.f64 (.f64 x (+.f64 1/2 y))) (sqrt.f64 (*.f64 x (+.f64 1/2 y))))
(.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (+.f64 1/2 y))))
(.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (-.f64 1/2 y))))
(.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (*.f64 x 1/2))))))
(/.f64 1 (/.f64 (.f64 x (-.f64 1/2 y)) (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))))
(/.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))) (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 (.f64 x y) 2) (-.f64 (.f64 (.f64 x x) 1/4) (.f64 x (.f64 1/2 (.f64 x y))))))
(/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (.f64 (.f64 x x) 1/4)) (-.f64 (.f64 x y) (*.f64 x 1/2)))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (-.f64 1/2 y))))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2))))))
(pow.f64 (*.f64 x (+.f64 1/2 y)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 1/2 y))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 1/2 y))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 1/2 y)))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y))))
(exp.f64 (log.f64 (*.f64 x (+.f64 1/2 y))))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 1/2 y))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 1/2 y))))
(fma.f64 x y (*.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 x y))
(fma.f64 y x (*.f64 x 1/2))
(fma.f64 1 (.f64 x 1/2) (.f64 x y))
(fma.f64 1 (.f64 x y) (.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 x y))
(fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (*.f64 x 1/2))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) 1/4)) (cbrt.f64 (.f64 x 1/2)) (.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) (*.f64 x 1/2))

Outputs
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(*.f64 (+.f64 1/2 y) x)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(*.f64 (+.f64 1/2 y) x)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(*.f64 (+.f64 1/2 y) x)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(*.f64 (+.f64 1/2 y) x)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 y) 1/2)))
(*.f64 (+.f64 1/2 y) x)
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 (+.f64 1/2 y) x)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y)))) 1)
(*.f64 (+.f64 1/2 y) x)
(-.f64 (/.f64 (.f64 (.f64 x x) 1/4) (.f64 x (-.f64 1/2 y))) (/.f64 (pow.f64 (.f64 x y) 2) (*.f64 x (-.f64 1/2 y))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(*.f64 x (+.f64 1/2 y))
(*.f64 (+.f64 1/2 y) x)
(*.f64 x (+.f64 y 1/2))
(*.f64 (+.f64 1/2 y) x)
(.f64 (.f64 x (+.f64 1/2 y)) 1)
(*.f64 (+.f64 1/2 y) x)
(.f64 1 (.f64 x (+.f64 1/2 y)))
(*.f64 (+.f64 1/2 y) x)
(.f64 (sqrt.f64 (.f64 x (+.f64 1/2 y))) (sqrt.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 2))
(*.f64 (+.f64 1/2 y) x)
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (-.f64 1/2 y))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (*.f64 x 1/2))))))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/8 (pow.f64 (.f64 y x) 3)) 1) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 y x) (.f64 x (-.f64 y 1/2)))))
(/.f64 (.f64 (pow.f64 x 3) (+.f64 1/8 (pow.f64 y 3))) (.f64 x (+.f64 (.f64 x 1/4) (.f64 (*.f64 y x) (+.f64 y -1/2)))))
(.f64 (/.f64 (pow.f64 x 3) x) (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 (.f64 y x) (+.f64 y -1/2) (*.f64 x 1/4))))
(/.f64 1 (/.f64 (.f64 x (-.f64 1/2 y)) (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(/.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))) (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/8 (pow.f64 (.f64 y x) 3)) 1) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 y x) (.f64 x (-.f64 y 1/2)))))
(/.f64 (.f64 (pow.f64 x 3) (+.f64 1/8 (pow.f64 y 3))) (.f64 x (+.f64 (.f64 x 1/4) (.f64 (*.f64 y x) (+.f64 y -1/2)))))
(.f64 (/.f64 (pow.f64 x 3) x) (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 (.f64 y x) (+.f64 y -1/2) (*.f64 x 1/4))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2)))))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/8 (pow.f64 (.f64 y x) 3)) 1) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 y x) (.f64 x (-.f64 y 1/2)))))
(/.f64 (.f64 (pow.f64 x 3) (+.f64 1/8 (pow.f64 y 3))) (.f64 x (+.f64 (.f64 x 1/4) (.f64 (*.f64 y x) (+.f64 y -1/2)))))
(.f64 (/.f64 (pow.f64 x 3) x) (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 (.f64 y x) (+.f64 y -1/2) (*.f64 x 1/4))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 (.f64 x y) 2) (-.f64 (.f64 (.f64 x x) 1/4) (.f64 x (.f64 1/2 (.f64 x y))))))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/8 (pow.f64 (.f64 y x) 3)) 1) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 y x) (.f64 x (-.f64 y 1/2)))))
(/.f64 (.f64 (pow.f64 x 3) (+.f64 1/8 (pow.f64 y 3))) (.f64 x (+.f64 (.f64 x 1/4) (.f64 (*.f64 y x) (+.f64 y -1/2)))))
(.f64 (/.f64 (pow.f64 x 3) x) (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 (.f64 y x) (+.f64 y -1/2) (*.f64 x 1/4))))
(/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (.f64 (.f64 x x) 1/4)) (-.f64 (.f64 x y) (*.f64 x 1/2)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (-.f64 1/2 y))))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/4) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/4)) (pow.f64 (.f64 y x) 2)) (.f64 x (-.f64 1/2 y)))
(/.f64 (.f64 (.f64 x x) (-.f64 1/4 (.f64 y y))) (.f64 x (-.f64 1/2 y)))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 (/.f64 (.f64 y y) -1) -1/4))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 1/8) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (.f64 (.f64 x x) 1/4) (.f64 (.f64 x y) (-.f64 (.f64 x y) (.f64 x 1/2))))))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/8 (pow.f64 (.f64 y x) 3)) 1) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 y x) (.f64 x (-.f64 y 1/2)))))
(/.f64 (.f64 (pow.f64 x 3) (+.f64 1/8 (pow.f64 y 3))) (.f64 x (+.f64 (.f64 x 1/4) (.f64 (*.f64 y x) (+.f64 y -1/2)))))
(.f64 (/.f64 (pow.f64 x 3) x) (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 (.f64 y x) (+.f64 y -1/2) (*.f64 x 1/4))))
(pow.f64 (*.f64 x (+.f64 1/2 y)) 1)
(*.f64 (+.f64 1/2 y) x)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 1/2 y))) 2)
(*.f64 (+.f64 1/2 y) x)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 1/2 y))) 3)
(*.f64 (+.f64 1/2 y) x)
(pow.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3) 1/3)
(*.f64 (+.f64 1/2 y) x)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 2))
(*.f64 (+.f64 1/2 y) x)
(log.f64 (exp.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 1/2 y)))))
(*.f64 (+.f64 1/2 y) x)
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 1/2 y)) 3))
(*.f64 (+.f64 1/2 y) x)
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(exp.f64 (log.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 1/2 y))) 1))
(*.f64 (+.f64 1/2 y) x)
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 1/2 y))))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 x y (*.f64 x 1/2))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 x 1/2 (*.f64 x y))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 y x (*.f64 x 1/2))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 1 (.f64 x 1/2) (.f64 x y))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 1 (.f64 x y) (.f64 x 1/2))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 x y))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (*.f64 x 1/2))
(*.f64 (+.f64 1/2 y) x)
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) 1/4)) (cbrt.f64 (.f64 x 1/2)) (.f64 x y))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) 1/4)) (cbrt.f64 (.f64 1/2 x)) (.f64 y x))
(fma.f64 (cbrt.f64 (.f64 x (.f64 x 1/4))) (cbrt.f64 (.f64 1/2 x)) (.f64 y x))
(fma.f64 y x (.f64 (cbrt.f64 (.f64 x (.f64 x 1/4))) (cbrt.f64 (.f64 1/2 x))))
(fma.f64 y x (.f64 (cbrt.f64 (.f64 (.f64 x x) 1/4)) (cbrt.f64 (.f64 1/2 x))))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) (*.f64 x 1/2))
(*.f64 (+.f64 1/2 y) x)

eval14.0ms (0.3%)

Compiler: Compiled 745 to 443 computations (40.5% saved)

prune10.0ms (0.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	53	7	60

Error

Counts

60 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))
✓	0.0b	(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
✓	30.9b	(+.f64 (/.f64 x 2) (*.f64 y x))
✓	16.0b	(+.f64 (/.f64 x 2) z)
▶	31.0b	(*.f64 (+.f64 1/2 y) x)
▶	47.5b	(*.f64 y x)
▶	46.1b	(*.f64 1/2 x)

Compiler

Compiled 61 to 43 computations (29.5% saved)

localize3.0ms (0.1%)

Compiler: Compiled 8 to 6 computations (25% saved)

localize3.0ms (0.1%)

Compiler: Compiled 8 to 4 computations (50% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1/2 y) x)

Compiler

Compiled 14 to 9 computations (35.7% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (+.f64 1/2 y) x)
0.0ms	x	@	-inf	(*.f64 (+.f64 1/2 y) x)
0.0ms	y	@	inf	(*.f64 (+.f64 1/2 y) x)
0.0ms	x	@	0	(*.f64 (+.f64 1/2 y) x)
0.0ms	y	@	0	(*.f64 (+.f64 1/2 y) x)

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1576×	`add-sqr-sqrt`
1554×	`*-un-lft-identity`
1456×	`add-cube-cbrt`
1440×	`add-cbrt-cube`
1426×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	150	13
2	1886	13

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y x) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 1/2 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 1/4 (*.f64 y y))) (-.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1/8 (pow.f64 y 3))) (+.f64 1/4 (*.f64 y (-.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/4 (*.f64 y y)) x) (-.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (pow.f64 y 3)) x) (+.f64 1/4 (*.f64 y (-.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 1/2 y) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 1/2 y) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 1/2 y) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 1/2 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 1/2 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 1/2 y) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 1/2 y) x)))))))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

976×	`*-commutative`
900×	`log-prod`
892×	`+-commutative`
882×	`fma-def`
766×	`associate-+r-`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	143	486
2	434	486
3	2382	486
4	4693	486
5	7408	486

Stop Event

1×	node limit

Counts

32 → 32

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 x 1/2) (.f64 x y))
(+.f64 (.f64 x y) (.f64 x 1/2))
(+.f64 (.f64 1/2 x) (.f64 y x))
(+.f64 (.f64 y x) (.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 (+.f64 1/2 y) x)) 1)
(/.f64 (.f64 x (-.f64 1/4 (.f64 y y))) (-.f64 1/2 y))
(/.f64 (.f64 x (+.f64 1/8 (pow.f64 y 3))) (+.f64 1/4 (.f64 y (-.f64 y 1/2))))
(/.f64 (.f64 (-.f64 1/4 (.f64 y y)) x) (-.f64 1/2 y))
(/.f64 (.f64 (+.f64 1/8 (pow.f64 y 3)) x) (+.f64 1/4 (.f64 y (-.f64 y 1/2))))
(pow.f64 (*.f64 (+.f64 1/2 y) x) 1)
(pow.f64 (sqrt.f64 (*.f64 (+.f64 1/2 y) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (+.f64 1/2 y) x)) 3)
(pow.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 1/2 y)))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 1/2 y) x)))
(exp.f64 (log.f64 (*.f64 (+.f64 1/2 y) x)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 1/2 y) x)) 1))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 1/2 y) x)))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(*.f64 y x)
(*.f64 x y)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(*.f64 y x)
(*.f64 x y)
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 x 1/2) (.f64 x y))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 x y) (.f64 x 1/2))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 y x))
(*.f64 x (+.f64 1/2 y))
(+.f64 (.f64 y x) (.f64 1/2 x))
(*.f64 x (+.f64 1/2 y))
(-.f64 (+.f64 1 (*.f64 (+.f64 1/2 y) x)) 1)
(*.f64 x (+.f64 1/2 y))
(/.f64 (.f64 x (-.f64 1/4 (.f64 y y))) (-.f64 1/2 y))
(/.f64 x (/.f64 (-.f64 1/2 y) (-.f64 1/4 (*.f64 y y))))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 1/4 (.f64 y y)))
(*.f64 (fma.f64 y (neg.f64 y) 1/4) (/.f64 x (-.f64 1/2 y)))
(.f64 x (/.f64 (-.f64 1/4 (.f64 y y)) (-.f64 1/2 y)))
(/.f64 (.f64 x (+.f64 1/8 (pow.f64 y 3))) (+.f64 1/4 (.f64 y (-.f64 y 1/2))))
(/.f64 x (/.f64 (+.f64 1/4 (*.f64 y (+.f64 y -1/2))) (+.f64 1/8 (pow.f64 y 3))))
(*.f64 (/.f64 x (fma.f64 y (+.f64 y -1/2) 1/4)) (+.f64 1/8 (pow.f64 y 3)))
(*.f64 x (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 y (+.f64 y -1/2) 1/4)))
(*.f64 (+.f64 1/8 (pow.f64 y 3)) (/.f64 x (fma.f64 y (+.f64 y -1/2) 1/4)))
(/.f64 (.f64 (-.f64 1/4 (.f64 y y)) x) (-.f64 1/2 y))
(/.f64 x (/.f64 (-.f64 1/2 y) (-.f64 1/4 (*.f64 y y))))
(.f64 (/.f64 x (-.f64 1/2 y)) (-.f64 1/4 (.f64 y y)))
(*.f64 (fma.f64 y (neg.f64 y) 1/4) (/.f64 x (-.f64 1/2 y)))
(.f64 x (/.f64 (-.f64 1/4 (.f64 y y)) (-.f64 1/2 y)))
(/.f64 (.f64 (+.f64 1/8 (pow.f64 y 3)) x) (+.f64 1/4 (.f64 y (-.f64 y 1/2))))
(/.f64 x (/.f64 (+.f64 1/4 (*.f64 y (+.f64 y -1/2))) (+.f64 1/8 (pow.f64 y 3))))
(*.f64 (/.f64 x (fma.f64 y (+.f64 y -1/2) 1/4)) (+.f64 1/8 (pow.f64 y 3)))
(*.f64 x (/.f64 (+.f64 1/8 (pow.f64 y 3)) (fma.f64 y (+.f64 y -1/2) 1/4)))
(*.f64 (+.f64 1/8 (pow.f64 y 3)) (/.f64 x (fma.f64 y (+.f64 y -1/2) 1/4)))
(pow.f64 (*.f64 (+.f64 1/2 y) x) 1)
(*.f64 x (+.f64 1/2 y))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 1/2 y) x)) 2)
(*.f64 x (+.f64 1/2 y))
(pow.f64 (cbrt.f64 (*.f64 (+.f64 1/2 y) x)) 3)
(*.f64 x (+.f64 1/2 y))
(pow.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3) 1/3)
(*.f64 x (+.f64 1/2 y))
(sqrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 2))
(*.f64 x (+.f64 1/2 y))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 1/2 y)))
(*.f64 x (+.f64 1/2 y))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 1/2 y) x) 3))
(*.f64 x (+.f64 1/2 y))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 1/2 y) x)))
(*.f64 x (+.f64 1/2 y))
(exp.f64 (log.f64 (*.f64 (+.f64 1/2 y) x)))
(*.f64 x (+.f64 1/2 y))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 1/2 y) x)) 1))
(*.f64 x (+.f64 1/2 y))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 1/2 y) x)))
(*.f64 x (+.f64 1/2 y))

eval7.0ms (0.2%)

Compiler: Compiled 292 to 193 computations (33.9% saved)

prune6.0ms (0.1%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	32	7	39

Error

Counts

39 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))
✓	0.0b	(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
✓	30.9b	(+.f64 (/.f64 x 2) (*.f64 y x))
✓	16.0b	(+.f64 (/.f64 x 2) z)
✓	31.0b	(*.f64 (+.f64 1/2 y) x)
✓	47.5b	(*.f64 y x)
✓	46.1b	(*.f64 1/2 x)

Compiler

Compiled 61 to 43 computations (29.5% saved)

regimes30.0ms (0.6%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 y x)
(*.f64 (+.f64 1/2 y) x)
(+.f64 (/.f64 x 2) z)
(+.f64 (/.f64 x 2) (*.f64 y x))
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
(+.f64 (/.f64 x 2) (fma.f64 x y z))

Outputs
(+.f64 (/.f64 x 2) (fma.f64 x y z))

Calls

5 calls:

6.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))
6.0ms	z
6.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
6.0ms	y
5.0ms	x

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`z`
0b	1	`(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)`
0b	1	`(+.f64 (/.f64 x 2) (*.f64 y x))`

Compiler

Compiled 86 to 52 computations (39.5% saved)

regimes28.0ms (0.6%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 y x)
(*.f64 (+.f64 1/2 y) x)
(+.f64 (/.f64 x 2) z)
(+.f64 (/.f64 x 2) (*.f64 y x))
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))

Outputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)

Calls

5 calls:

6.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))
5.0ms	y
5.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
5.0ms	z
5.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`z`
0.0b	1	`(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)`
0.0b	1	`(+.f64 (/.f64 x 2) (*.f64 y x))`

Compiler

Compiled 78 to 48 computations (38.5% saved)

regimes2.2s (47.6%)

Counts

5 → 5

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 y x)
(*.f64 (+.f64 1/2 y) x)
(+.f64 (/.f64 x 2) z)
(+.f64 (/.f64 x 2) (*.f64 y x))

Outputs
(+.f64 (/.f64 x 2) z)
(+.f64 (/.f64 x 2) (*.f64 y x))
(+.f64 (/.f64 x 2) z)
(*.f64 y x)
(+.f64 (/.f64 x 2) z)

Calls

4 calls:

2.2s	z
22.0ms	x
16.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))
8.0ms	y

Results

Error	Segments	Branch
12.0b	5	`x`
9.9b	2	`y`
7.6b	5	`z`
10.0b	3	`(+.f64 (/.f64 x 2) (*.f64 y x))`

Compiler

Compiled 48 to 31 computations (35.4% saved)

bsearch55.0ms (1.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
16.0ms	0.060281542954232666	54645.164987994496
12.0ms	3.2937629610797612e-15	1.0071456183506415e-13
10.0ms	1.119411572649373e-131	1.4059297842063007e-130
17.0ms	-3.9760703463976915e-13	-3.977474130108523e-21

Results

49.0ms

496×

body

256

valid

Compiler

Compiled 574 to 430 computations (25.1% saved)

regimes90.0ms (1.9%)

Counts

4 → 5

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 y x)
(*.f64 (+.f64 1/2 y) x)
(+.f64 (/.f64 x 2) z)

Outputs
(+.f64 (/.f64 x 2) z)
(*.f64 (+.f64 1/2 y) x)
(+.f64 (/.f64 x 2) z)
(*.f64 y x)
(+.f64 (/.f64 x 2) z)

Calls

3 calls:

61.0ms	x
19.0ms	z
8.0ms	y

Results

Error	Segments	Branch
12.0b	5	`x`
9.9b	2	`y`
7.6b	5	`z`

Compiler

Compiled 31 to 21 computations (32.3% saved)

bsearch104.0ms (2.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
39.0ms	0.060281542954232666	54645.164987994496
13.0ms	3.2937629610797612e-15	1.0071456183506415e-13
10.0ms	1.119411572649373e-131	1.4059297842063007e-130
41.0ms	-3.9760703463976915e-13	-3.977474130108523e-21

Results

98.0ms

496×

body

256

valid

Compiler

Compiled 544 to 415 computations (23.7% saved)

regimes14.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	y
4.0ms	z
3.0ms	x

Results

Error	Segments	Branch
31.0b	1	`x`
31.0b	1	`y`
31.0b	1	`z`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes76.0ms (1.6%)

Accuracy

Total -30.5b remaining (-96.3%)

Threshold costs -30.5b (-96.3%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

3 calls:

52.0ms	z
14.0ms	x
8.0ms	y

Results

Error	Segments	Branch
38.5b	5	`x`
31.7b	3	`y`
40.2b	8	`z`

Compiler

Compiled 21 to 15 computations (28.6% saved)

bsearch32.0ms (0.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	0.00021873176832989987	387952.17241149256
16.0ms	-734.1409798760662	-0.0002781976434847886

Results

27.0ms

288×

body

256

valid

Compiler

Compiled 270 to 211 computations (21.9% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative`
6×	`if-if-or-not`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	289
1	65	289

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (/.f64 x 2) (fma.f64 x y z))
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(if (<=.f64 z -1298074214633707/324518553658426726783156020576256) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (+.f64 (/.f64 x 2) (.f64 y x)) (if (<=.f64 z 3961408125713217/39614081257132168796771975168) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 58) (.f64 y x) (+.f64 (/.f64 x 2) z)))))
(if (<=.f64 z -5399988732876221/41538374868278621028243970633760768) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 (+.f64 1/2 y) x) (if (<=.f64 z 3961408125713217/39614081257132168796771975168) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 3152519739159347/9007199254740992) (.f64 y x) (+.f64 (/.f64 x 2) z)))))
(*.f64 (+.f64 1/2 y) x)
(if (<=.f64 y -1/2) (.f64 y x) (if (<=.f64 y 1/2) (.f64 1/2 x) (*.f64 y x)))
(*.f64 1/2 x)

Outputs
(+.f64 (/.f64 x 2) (fma.f64 x y z))
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 z (+.f64 (/.f64 x 2) (*.f64 x y)))
(if (<=.f64 z -1298074214633707/324518553658426726783156020576256) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (+.f64 (/.f64 x 2) (.f64 y x)) (if (<=.f64 z 3961408125713217/39614081257132168796771975168) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 58) (.f64 y x) (+.f64 (/.f64 x 2) z)))))
(if (<=.f64 z -1298074214633707/324518553658426726783156020576256) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (+.f64 (/.f64 x 2) (.f64 x y)) (if (or (<=.f64 z 3961408125713217/39614081257132168796771975168) (not (<=.f64 z 58))) (+.f64 (/.f64 x 2) z) (.f64 x y))))
(if (<=.f64 z -5399988732876221/41538374868278621028243970633760768) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 (+.f64 1/2 y) x) (if (<=.f64 z 3961408125713217/39614081257132168796771975168) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 3152519739159347/9007199254740992) (.f64 y x) (+.f64 (/.f64 x 2) z)))))
(if (<=.f64 z -5399988732876221/41538374868278621028243970633760768) (+.f64 (/.f64 x 2) z) (if (<=.f64 z 6992716752707823/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 x (+.f64 y 1/2)) (if (or (<=.f64 z 3961408125713217/39614081257132168796771975168) (not (<=.f64 z 3152519739159347/9007199254740992))) (+.f64 (/.f64 x 2) z) (.f64 x y))))
(*.f64 (+.f64 1/2 y) x)
(*.f64 x (+.f64 y 1/2))
(if (<=.f64 y -1/2) (.f64 y x) (if (<=.f64 y 1/2) (.f64 1/2 x) (*.f64 y x)))
(if (<=.f64 y -1/2) (.f64 x y) (if (<=.f64 y 1/2) (.f64 x 1/2) (*.f64 x y)))
(*.f64 1/2 x)
(*.f64 x 1/2)

Compiler

Compiled 135 to 90 computations (33.3% saved)

soundness42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

12×	`fma-def`
12×	`+-commutative`
4×	`associate-+l+`
2×	`associate-+r+`
2×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	15	21
2	26	21
3	29	21

Stop Event

1×

saturated

Compiler

Compiled 38 to 21 computations (44.7% saved)

end110.0ms (2.4%)

Compiler: Compiled 117 to 69 computations (41% saved)

Details

analyze347.0ms (7.5%)

sample1.0s (22%)

preprocess11.0ms (0.2%)

simplify11.0ms (0.2%)

eval2.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite53.0ms (1.1%)

simplify56.0ms (1.2%)

localize8.0ms (0.2%)

eval11.0ms (0.2%)

prune7.0ms (0.2%)

localize6.0ms (0.1%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite59.0ms (1.3%)

simplify59.0ms (1.3%)

eval14.0ms (0.3%)

prune10.0ms (0.2%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite50.0ms (1.1%)

simplify69.0ms (1.5%)

eval7.0ms (0.2%)

prune6.0ms (0.1%)

regimes30.0ms (0.6%)

regimes28.0ms (0.6%)

regimes2.2s (47.6%)

bsearch55.0ms (1.2%)

regimes90.0ms (1.9%)

bsearch104.0ms (2.2%)

regimes14.0ms (0.3%)

regimes76.0ms (1.6%)

bsearch32.0ms (0.7%)

simplify9.0ms (0.2%)

soundness42.0ms (0.9%)

end110.0ms (2.4%)

Profiling