Details

analyze195.0ms (3.9%)

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
28.1%	28.1%	71.8%	0.1%	0%	0%	0%	9
37.6%	34.3%	56.9%	0.1%	8.6%	0%	0%	10
44.8%	40.6%	49.9%	0.1%	9.4%	0%	0%	11
53.4%	48%	41.9%	0.1%	9.9%	0%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.9s (37.6%)

Results

1.6s	8254×	body	256	valid
244.0ms	1158×	body	256	infinite
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Bogosity

preprocess78.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

522×	`fma-def_binary64`
97×	`distribute-rgt-in_binary64`
78×	`associate-+l+_binary64`
66×	`associate-+r+_binary64`
61×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	53	40
2	137	40
3	336	40
4	706	40
5	1090	40
6	1156	40
7	1162	40
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

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

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

Symmetry

(sort x y)

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify20.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
32×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
20×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	51	10
3	120	10
4	246	10
5	386	10
6	408	10
7	410	10

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% 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 (+.f64 x y) (+.f64 z 1))

Compiler

Compiled 10 to 7 computations (30% saved)

localize93.0ms (1.9%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 10 computations (50% saved)

series11.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	z	@	0	(*.f64 (+.f64 x y) (+.f64 z 1))
1.0ms	x	@	inf	(*.f64 (+.f64 x y) (+.f64 z 1))
1.0ms	x	@	0	(*.f64 (+.f64 x y) (+.f64 z 1))
1.0ms	y	@	inf	(*.f64 (+.f64 x y) (+.f64 z 1))
1.0ms	z	@	inf	(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite150.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

676×	`prod-diff_binary64`
600×	`unpow-prod-down_binary64`
408×	`log-prod_binary64`
324×	`fma-def_binary64`
231×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	176	10
2	2546	10

Stop Event

1×	node limit

Counts

1 → 76

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x y) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (+.f64 x y) (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 x y) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (+.f64 x y) z) 1) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 z 1)) (.f64 y (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (+.f64 z 1)) (.f64 x (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 z 1) x) (.f64 (+.f64 z 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 z 1) y) (.f64 (+.f64 z 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 x y) z x) y)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 x y) z y) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (+.f64 x y) (+.f64 z 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 1 (pow.f64 z 3))) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (-.f64 (fma.f64 z z 1) z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (+.f64 1 (pow.f64 z 3))) (.f64 (-.f64 x y) (-.f64 (fma.f64 z z 1) z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (fma.f64 z z -1)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (-.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (fma.f64 z z -1)) (.f64 (-.f64 x y) (-.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 z 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (-.f64 (fma.f64 z z 1) z) (fma.f64 y (-.f64 y x) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 z z -1) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (-.f64 z 1) (fma.f64 y (-.f64 y x) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 z 3)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (-.f64 (fma.f64 z z 1) z) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 z z -1) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (-.f64 z 1) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (+.f64 x y) z) 3) (pow.f64 (+.f64 x y) 3)) (+.f64 (pow.f64 (.f64 (+.f64 x y) z) 2) (-.f64 (pow.f64 (+.f64 x y) 2) (.f64 (.f64 (+.f64 x y) z) (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 (+.f64 x y) z) 2) (pow.f64 (+.f64 x y) 2)) (-.f64 (.f64 (+.f64 x y) z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 z 1)) (fma.f64 y (-.f64 y x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (+.f64 z 1)) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 z 3)) (+.f64 x y)) (-.f64 (fma.f64 z z 1) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 z z -1) (+.f64 x y)) (-.f64 z 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 x y) (+.f64 1 (pow.f64 z 3))) (-.f64 (fma.f64 z z 1) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 x y) (fma.f64 z z -1)) (-.f64 z 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 z 1) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 z 1) (.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 x y) (+.f64 z 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (+.f64 x y) (+.f64 z 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (+.f64 x y) (+.f64 z 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (+.f64 x y) (+.f64 z 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (+.f64 x y) (+.f64 z 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (+.f64 x y) (+.f64 z 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (+.f64 x y) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (+.f64 x y)) (exp.f64 (.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x y))) (exp.f64 (.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 (+.f64 x y) z)) (+.f64 1 (expm1.f64 (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (+.f64 x y) (+.f64 z 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (+.f64 x y) (+.f64 z 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (+.f64 x y) (+.f64 z 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 z) (log.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (+.f64 (log1p.f64 z) (log.f64 (+.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 z 1) (.f64 y (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (+.f64 z 1) (.f64 x (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x y) z (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x y) 1 (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z (+.f64 x y) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x y) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (+.f64 x y) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 z 1) x (.f64 (+.f64 z 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 z 1) y (.f64 (+.f64 z 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x y)) (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (cbrt.f64 (+.f64 x y)) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) 1) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 x y)) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) 1) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 1 (fma.f64 y (-.f64 y x) (.f64 x x))) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 x y) (-.f64 x y)) (/.f64 1 (-.f64 x y)) (.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 x y) z) 1 (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) 2) (cbrt.f64 (.f64 (+.f64 x y) z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (.f64 (+.f64 x y) z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x y))) (.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x y))) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 z)) (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 z (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (cbrt.f64 (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 z (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 x y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 x y) (sqrt.f64 z)) (sqrt.f64 z) (+.f64 x y))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x y) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 x y) (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x y) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (+.f64 x y) z) 1) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 z 1)) (*.f64 y (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 z 1)) (*.f64 x (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 z 1) x) (*.f64 (+.f64 z 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 z 1) y) (*.f64 (+.f64 z 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 x y) z x) y)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 x y) z y) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (+.f64 z 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 1 (pow.f64 z 3))) (*.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (-.f64 (fma.f64 z z 1) z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (+.f64 1 (pow.f64 z 3))) (*.f64 (-.f64 x y) (-.f64 (fma.f64 z z 1) z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (fma.f64 z z -1)) (*.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (-.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (fma.f64 z z -1)) (*.f64 (-.f64 x y) (-.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 z 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (-.f64 (fma.f64 z z 1) z) (fma.f64 y (-.f64 y x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 z z -1) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (-.f64 z 1) (fma.f64 y (-.f64 y x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 z 3)) (*.f64 (+.f64 x y) (-.f64 x y))) (*.f64 (-.f64 (fma.f64 z z 1) z) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 z z -1) (*.f64 (+.f64 x y) (-.f64 x y))) (*.f64 (-.f64 z 1) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3) (pow.f64 (+.f64 x y) 3)) (+.f64 (pow.f64 (*.f64 (+.f64 x y) z) 2) (-.f64 (pow.f64 (+.f64 x y) 2) (*.f64 (*.f64 (+.f64 x y) z) (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 (+.f64 x y) z) 2) (pow.f64 (+.f64 x y) 2)) (-.f64 (*.f64 (+.f64 x y) z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 z 1)) (fma.f64 y (-.f64 y x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (+.f64 z 1)) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 z 3)) (+.f64 x y)) (-.f64 (fma.f64 z z 1) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 z z -1) (+.f64 x y)) (-.f64 z 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x y) (+.f64 1 (pow.f64 z 3))) (-.f64 (fma.f64 z z 1) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x y) (fma.f64 z z -1)) (-.f64 z 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 z 1) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 z 1) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) (+.f64 z 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 z 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 z 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) (+.f64 z 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 z 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 z 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 x y) (+.f64 z 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 x y)) (exp.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x y))) (exp.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 (+.f64 x y) z)) (+.f64 1 (expm1.f64 (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 z 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (+.f64 z 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (+.f64 z 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 z) (log.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log1p.f64 z) (log.f64 (+.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (+.f64 z 1) (*.f64 x (+.f64 z 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x y) z (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x y) 1 (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z (+.f64 x y) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x y) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (+.f64 x y) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 z 1) x (*.f64 (+.f64 z 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 z 1) y (*.f64 (+.f64 z 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x y)) (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (cbrt.f64 (+.f64 x y)) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) 1) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 x y)) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (sqrt.f64 (+.f64 x y)) 1) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (sqrt.f64 (+.f64 x y)) z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 1 (fma.f64 y (-.f64 y x) (*.f64 x x))) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (/.f64 1 (-.f64 x y)) (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x y) z) 1 (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 2) (cbrt.f64 (*.f64 (+.f64 x y) z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x y))) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 z)) (*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 z)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (cbrt.f64 (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x y) (sqrt.f64 z)) (sqrt.f64 z) (+.f64 x y))))))

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

176×	`fma-def_binary64`
37×	`associate-+l+_binary64`
25×	`associate-+r+_binary64`
20×	`distribute-rgt-in_binary64`
15×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	438
1	33	330
2	71	318
3	164	318
4	279	318
5	325	318
6	359	318
7	365	318

Stop Event

1×

saturated

Counts

112 → 86

Calls

Call 1

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

Outputs
(*.f64 y (+.f64 1 z))
(+.f64 y (*.f64 y z))
(fma.f64 y z y)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 y (+.f64 1 z))
(+.f64 y (*.f64 y z))
(fma.f64 y z y)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 y (+.f64 1 z))
(+.f64 y (*.f64 y z))
(fma.f64 y z y)
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 (.f64 (+.f64 1 z) x) (.f64 y (+.f64 1 z)))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y x)
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 (+.f64 y x) z)
(*.f64 z (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(*.f64 (+.f64 y x) z)
(*.f64 z (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))
(+.f64 y (+.f64 (*.f64 (+.f64 y x) z) x))
(fma.f64 (+.f64 1 z) x (*.f64 y (+.f64 1 z)))
(*.f64 (+.f64 1 z) (+.f64 y x))

eval19.0ms (0.4%)

Compiler: Compiled 1162 to 452 computations (61.1% saved)

prune44.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	7	87

Error

Counts

87 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	40.2b	(*.f64 (+.f64 y x) z)
▶	34.1b	(*.f64 y (+.f64 1 z))
	0.0b	(+.f64 (+.f64 x y) (*.f64 (+.f64 x y) z))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
▶	0.0b	(+.f64 (.f64 (+.f64 z 1) y) (.f64 (+.f64 z 1) x))
▶	23.2b	(+.f64 y x)
▶	28.9b	(*.f64 (+.f64 1 z) x)

Compiler

Compiled 122 to 81 computations (33.6% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 31 to 19 computations (38.7% saved)

series5.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

791×	`pow1_binary64`
730×	`log1p-expm1-u_binary64`
730×	`expm1-log1p-u_binary64`
729×	`add-log-exp_binary64`
714×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	161	14
2	2017	14

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

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

Outputs

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

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

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
4×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	228
1	29	228
2	39	228
3	58	228
4	66	228
5	70	228

Stop Event

1×

saturated

Counts

90 → 52

Calls

Call 1

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

Outputs
x
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(fma.f64 z x x)
(fma.f64 x z x)
y
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y z)
(*.f64 z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y z)
(*.f64 z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)
(*.f64 y (+.f64 1 z))
(fma.f64 y z y)
(fma.f64 z y y)

localize3.0ms (0.1%)

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (+.f64 1 z))

Compiler

Compiled 14 to 9 computations (35.7% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(*.f64 y (+.f64 1 z))
0.0ms	z	@	inf	(*.f64 y (+.f64 1 z))
0.0ms	y	@	inf	(*.f64 y (+.f64 1 z))
0.0ms	z	@	-inf	(*.f64 y (+.f64 1 z))
0.0ms	y	@	-inf	(*.f64 y (+.f64 1 z))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

643×	`pow1_binary64`
598×	`add-log-exp_binary64`
598×	`log1p-expm1-u_binary64`
598×	`expm1-log1p-u_binary64`
585×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	7
2	1666	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(*.f64 y (+.f64 1 z))

Outputs

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`
3×	`*-lft-identity_binary64`
3×	`*-rgt-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	54
1	8	54
2	12	54
3	16	54
4	22	54
5	28	54
6	41	54
7	45	54
8	47	54

Stop Event

1×

saturated

Counts

38 → 29

Calls

Call 1

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

Outputs
y
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(*.f64 y z)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(*.f64 y z)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)
(+.f64 (*.f64 y z) y)
(fma.f64 y z y)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 z) x)

Compiler

Compiled 14 to 9 computations (35.7% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	z	@	0	(*.f64 (+.f64 1 z) x)
0.0ms	z	@	-inf	(*.f64 (+.f64 1 z) x)
0.0ms	x	@	-inf	(*.f64 (+.f64 1 z) x)
0.0ms	z	@	inf	(*.f64 (+.f64 1 z) x)
0.0ms	x	@	inf	(*.f64 (+.f64 1 z) x)

rewrite56.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

604×	`pow1_binary64`
560×	`add-log-exp_binary64`
560×	`log1p-expm1-u_binary64`
560×	`expm1-log1p-u_binary64`
549×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1520	7

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(*.f64 (+.f64 1 z) x)

Outputs

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

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`
3×	`*-lft-identity_binary64`
3×	`*-rgt-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	54
1	11	54
2	16	54
3	22	54
4	28	54
5	41	54
6	45	54
7	47	54

Stop Event

1×

saturated

Counts

31 → 23

Calls

Call 1

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

Outputs
x
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)
(+.f64 (*.f64 z x) x)
(fma.f64 z x x)
(fma.f64 x z x)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 5 computations (64.3% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

9 calls:

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

rewrite47.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

715×	`pow1_binary64`
663×	`add-log-exp_binary64`
663×	`log1p-expm1-u_binary64`
663×	`expm1-log1p-u_binary64`
648×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1776	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
4×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	11	150
2	18	150
3	20	150

Stop Event

1×

saturated

Counts

45 → 26

Calls

Call 1

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

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

eval160.0ms (3.2%)

Compiler: Compiled 1329 to 627 computations (52.8% saved)

prune25.0ms (0.5%)

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	1	0	1
Picked	0	1	1
Done	1	4	5
Total	126	11	137

Error

Counts

137 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	40.2b	(+.f64 (.f64 z y) (.f64 z x))
▶	28.9b	(+.f64 (*.f64 z x) x)
	41.1b	x
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	40.2b	(*.f64 (+.f64 y x) z)
✓	34.1b	(*.f64 y (+.f64 1 z))
	44.8b	y
▶	52.0b	(*.f64 z y)
✓	23.2b	(+.f64 y x)
✓	28.9b	(*.f64 (+.f64 1 z) x)
▶	50.8b	(*.f64 z x)

Compiler

Compiled 78 to 53 computations (32.1% saved)

localize3.0ms (0.1%)

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

localize3.0ms (0.1%)

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 5 computations (61.5% saved)

series77.0ms (1.6%)

Counts

1 → 15

Calls

6 calls:

Time	Variable		Point	Expression
75.0ms	x	@	inf	(+.f64 (*.f64 z x) x)
1.0ms	x	@	-inf	(+.f64 (*.f64 z x) x)
0.0ms	z	@	0	(+.f64 (*.f64 z x) x)
0.0ms	x	@	0	(+.f64 (*.f64 z x) x)
0.0ms	z	@	inf	(+.f64 (*.f64 z x) x)

rewrite47.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`pow1_binary64`
590×	`add-log-exp_binary64`
589×	`log1p-expm1-u_binary64`
589×	`expm1-log1p-u_binary64`
577×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	112	5
2	1610	5

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-def_binary64`
53×	`fma-neg_binary64`
20×	`unsub-neg_binary64`
16×	`distribute-lft-in_binary64`
16×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	93
1	27	93
2	58	69
3	139	69
4	236	69
5	334	69
6	394	69

Stop Event

1×

saturated

Counts

55 → 45

Calls

Call 1

Inputs
x
(*.f64 z x)
(*.f64 z x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(*.f64 (+.f64 1 z) x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))

Outputs
x
(*.f64 z x)
(*.f64 x z)
(*.f64 z x)
(*.f64 x z)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(*.f64 (+.f64 1 z) x)
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 z) 1) x))
(*.f64 x (+.f64 z 1))
(fma.f64 x z x)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 6 computations (68.4% saved)

series5.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	z	@	inf	(+.f64 (.f64 z y) (.f64 z x))
1.0ms	z	@	0	(+.f64 (.f64 z y) (.f64 z x))
1.0ms	z	@	-inf	(+.f64 (.f64 z y) (.f64 z x))
0.0ms	y	@	0	(+.f64 (.f64 z y) (.f64 z x))
0.0ms	y	@	inf	(+.f64 (.f64 z y) (.f64 z x))

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

836×	`pow1_binary64`
774×	`add-log-exp_binary64`
774×	`log1p-expm1-u_binary64`
774×	`expm1-log1p-u_binary64`
757×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	151	7
2	2106	7

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

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

Outputs

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

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

90×	`fma-neg_binary64`
85×	`fma-def_binary64`
42×	`cancel-sign-sub-inv_binary64`
38×	`distribute-rgt-in_binary64`
34×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	234
1	34	234
2	80	234
3	210	234
4	434	234
5	567	234
6	677	234
7	682	234

Stop Event

1×

saturated

Counts

77 → 46

Calls

Call 1

Inputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(*.f64 z x)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 z x)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 z x)
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))
(+.f64 (.f64 y z) (.f64 z x))

Outputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(.f64 -1 (.f64 (+.f64 (.f64 -1 x) (.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (.f64 y z) (.f64 z x))
(*.f64 (+.f64 y x) z)

eval49.0ms (1%)

Compiler: Compiled 1029 to 368 computations (64.2% saved)

prune17.0ms (0.3%)

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	1	2
Picked	0	1	1
Done	0	8	8
Total	91	11	102

Error

Counts

102 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	40.2b	(+.f64 (.f64 z y) (.f64 z x))
✓	28.9b	(+.f64 (*.f64 z x) x)
✓	40.2b	(*.f64 (+.f64 y x) z)
✓	34.1b	(*.f64 y (+.f64 1 z))
	44.8b	y
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	52.0b	(*.f64 z y)
✓	23.2b	(+.f64 y x)
✓	28.9b	(*.f64 (+.f64 1 z) x)
	41.1b	x
✓	50.8b	(*.f64 z x)

Compiler

Compiled 78 to 53 computations (32.1% saved)

eval10.0ms (0.2%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune4.0ms (0.1%)

Pruning

11 alts after pruning (2 fresh and 9 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	9	9
Total	11	11

Error

Counts

11 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	40.2b	(+.f64 (.f64 z y) (.f64 z x))
✓	28.9b	(+.f64 (*.f64 z x) x)
✓	40.2b	(*.f64 (+.f64 y x) z)
✓	34.1b	(*.f64 y (+.f64 1 z))
	44.8b	y
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	52.0b	(*.f64 z y)
✓	23.2b	(+.f64 y x)
✓	28.9b	(*.f64 (+.f64 1 z) x)
	41.1b	x
✓	50.8b	(*.f64 z x)

Compiler

Compiled 78 to 53 computations (32.1% saved)

regimes126.0ms (2.5%)

Counts

14 → 1

Calls

Call 1

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

Outputs
(+.f64 (.f64 (+.f64 z 1) y) (.f64 (+.f64 z 1) x))

Calls

7 calls:

47.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))
33.0ms	(+.f64 x y)
12.0ms	y
10.0ms	x
8.0ms	z

Results

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

Compiler

Compiled 109 to 57 computations (47.7% saved)

regimes90.0ms (1.8%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

6 calls:

46.0ms	(+.f64 x y)
10.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))
9.0ms	x
9.0ms	z
8.0ms	y

Results

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

Compiler

Compiled 92 to 46 computations (50% saved)

regimes132.0ms (2.7%)

Counts

11 → 3

Calls

Call 1

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

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

Calls

3 calls:

77.0ms	x
28.0ms	y
25.0ms	z

Results

Error	Segments	Branch
7.3b	6	`x`
7.5b	4	`y`
1.8b	3	`z`

Compiler

Compiled 54 to 24 computations (55.6% saved)

bsearch69.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.583013194625646e-6	20943.138695808382
51.0ms	-15.303115969212687	-0.00031970680723839056

Compiler

Compiled 16 to 12 computations (25% saved)

regimes120.0ms (2.4%)

Counts

10 → 3

Calls

Call 1

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

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

Calls

3 calls:

73.0ms	x
26.0ms	y
18.0ms	z

Results

Error	Segments	Branch
7.3b	6	`x`
7.5b	4	`y`
1.8b	3	`z`

Compiler

Compiled 47 to 23 computations (51.1% saved)

bsearch54.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
32.0ms	1.583013194625646e-6	20943.138695808382
22.0ms	-15.303115969212687	-0.00031970680723839056

Compiler

Compiled 16 to 12 computations (25% saved)

regimes86.0ms (1.7%)

Counts

7 → 5

Calls

Call 1

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

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

Calls

3 calls:

30.0ms	x
29.0ms	z
25.0ms	y

Results

Error	Segments	Branch
14.0b	6	`x`
11.1b	5	`y`
9.3b	5	`z`

Compiler

Compiled 32 to 16 computations (50% saved)

bsearch92.0ms (1.9%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
26.0ms	1.425713496316878e+149	7.439277030266898e+160
30.0ms	1.4698149742790986e+89	1.5943976639714983e+91
20.0ms	5.433436965224155e-8	7.358124168936658e-8
16.0ms	-15.303115969212687	-0.00031970680723839056

Compiler

Compiled 268 to 189 computations (29.5% saved)

regimes99.0ms (2%)

Counts

6 → 5

Calls

Call 1

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

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

Calls

3 calls:

34.0ms	z
31.0ms	y
31.0ms	x

Results

Error	Segments	Branch
19.5b	7	`x`
18.4b	7	`y`
10.2b	5	`z`

Compiler

Compiled 27 to 15 computations (44.4% saved)

bsearch86.0ms (1.7%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
25.0ms	1.425713496316878e+149	7.439277030266898e+160
28.0ms	1.4698149742790986e+89	1.5943976639714983e+91
17.0ms	270206751336766.94	4.342690195538808e+19
16.0ms	-15.303115969212687	-0.00031970680723839056

Compiler

Compiled 254 to 182 computations (28.3% saved)

regimes120.0ms (2.4%)

Counts

5 → 10

Calls

Call 1

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

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

Calls

3 calls:

55.0ms	x
41.0ms	z
22.0ms	y

Results

Error	Segments	Branch
23.4b	10	`x`
24.3b	5	`y`
23.5b	9	`z`

Compiler

Compiled 24 to 14 computations (41.7% saved)

bsearch155.0ms (3.1%)

Algorithm

9×	binary-search

Steps

Time	Left	Right
18.0ms	2.2052204904392726e-194	1.2201825573305447e-180
17.0ms	6.524441548579088e-249	2.6755281106814303e-243
18.0ms	-6.1000904002789235e-297	-2.504060022870348e-297
18.0ms	-8.532215810813412e-235	-4.335269673525005e-237
17.0ms	-3.128975607685937e-159	-2.0455290131678964e-163
17.0ms	-7.158383172982673e-128	-1.3755812705927136e-128
17.0ms	-1.2687757937850129e-39	-2.474233920386677e-40
17.0ms	-3.6635552285502295e-26	-1.3582823022049778e-28
17.0ms	-5975658112521703.0	-20008430030289.57

Compiler

Compiled 16 to 12 computations (25% saved)

regimes68.0ms (1.4%)

Counts

4 → 3

Calls

Call 1

Inputs
x
x
y
(*.f64 z y)

Outputs
x
(*.f64 z y)
y

Calls

3 calls:

28.0ms	z
24.0ms	x
14.0ms	y

Results

Error	Segments	Branch
26.1b	6	`x`
25.9b	3	`y`
26.7b	7	`z`

Compiler

Compiled 21 to 13 computations (38.1% saved)

bsearch40.0ms (0.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	2.434344790719922e+52	1.2307321917494122e+54
21.0ms	2.225984573575691e-87	3.634806658030802e-81

Compiler

Compiled 16 to 12 computations (25% saved)

regimes40.0ms (0.8%)

Counts

3 → 2

Calls

Call 1

Inputs
x
x
y

Outputs
x
y

Calls

3 calls:

19.0ms	z
13.0ms	y
8.0ms	x

Results

Error	Segments	Branch
28.6b	2	`x`
28.9b	2	`y`
36.7b	5	`z`

Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch17.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-3.128975607685937e-159	-2.0455290131678964e-163

Compiler

Compiled 16 to 12 computations (25% saved)

regimes12.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

3 calls:

4.0ms	y
3.0ms	x
3.0ms	z

Results

Error	Segments	Branch
41.1b	1	`x`
41.1b	1	`y`
41.1b	1	`z`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	286
1	89	286

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (+.f64 z 1) y) (.f64 (+.f64 z 1) x))
(*.f64 (+.f64 x y) (+.f64 z 1))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 (+.f64 y x) z) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (+.f64 (.f64 z y) (*.f64 z x))))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 (+.f64 y x) z) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (.f64 (+.f64 y x) z)))
(if (<=.f64 z -4307444211034609/281474976710656) (+.f64 (.f64 z x) x) (if (<=.f64 z 2052694448908761/37778931862957161709568) (+.f64 y x) (if (<=.f64 z 150000000000000006280438121901244716806881918647697326742848129600338295293886572875743232) (+.f64 (.f64 z x) x) (if (<=.f64 z 74000000000000003292675868419441773450016658715608051850259778035325822929243804117411062511706674173316427036527874854277988879865182730538943771372700057993216) (.f64 z y) (.f64 z x)))))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 z x) (if (<=.f64 z 4323308021388271/16) (+.f64 y x) (if (<=.f64 z 150000000000000006280438121901244716806881918647697326742848129600338295293886572875743232) (.f64 z x) (if (<=.f64 z 74000000000000003292675868419441773450016658715608051850259778035325822929243804117411062511706674173316427036527874854277988879865182730538943771372700057993216) (.f64 z y) (.f64 z x)))))
(if (<=.f64 x -5975658112521703) x (if (<=.f64 x -6382813411925257/174224571863520493293247799005065324265472) (.f64 z x) (if (<=.f64 x -7777572985336443/6129982163463555433433388108601236734474956488734408704) x (if (<=.f64 x -6983335091520329/97554642197374757230674913431036447054643691958280348464348654988292866838117675628759565720734124098744591597543956965482749239977758915821568) (.f64 z x) (if (<=.f64 x -386945396624257/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568) x (if (<=.f64 x -190901022513733/223741436863085634409521749481834675708763587282583222886261325799305187541819563744885033326754909183041871165773435313081225474664635755472226765949723278285256830531087594548959384855304521689414375064310509745905707450052637371994990524269330432) y (if (<=.f64 x -35091490030787/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912) (.f64 z y) (if (<=.f64 x 1643575090803453/251910462920982955146951572855242064723418868082104455055218081010186148908960752236565235084370225856148908135059894885483907489539473312974233140212507046179002134322645704349866637075627537275802723363977045251916898867011814946574400376685636747593659677933568) y (if (<=.f64 x 7249849670368581/328758493846773344202561867680008041596896237676448366218642556441795759643567551382104158517349278201686435553511138607063714515636487741445488423165742553122201479445527787386978984867770169829455828233486336) (.f64 z y) y)))))))))
(if (<=.f64 y 4985637244835055/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776) x (if (<=.f64 y 24343447907199218469252872089856837939759052555812864) (*.f64 z y) y))
(if (<=.f64 x -386945396624257/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568) x y)
x

Outputs
(+.f64 (.f64 (+.f64 z 1) y) (.f64 (+.f64 z 1) x))
(*.f64 (+.f64 x y) (+.f64 z 1))
(*.f64 (+.f64 z 1) (+.f64 y x))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 (+.f64 y x) z) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (+.f64 (.f64 z y) (*.f64 z x))))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 z (+.f64 y x)) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (+.f64 (.f64 z y) (*.f64 z x))))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 (+.f64 y x) z) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (.f64 (+.f64 y x) z)))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 z (+.f64 y x)) (if (<=.f64 z 7475568452240553/4722366482869645213696) (+.f64 y x) (.f64 z (+.f64 y x))))
(if (<=.f64 z -4307444211034609/281474976710656) (+.f64 (.f64 z x) x) (if (<=.f64 z 2052694448908761/37778931862957161709568) (+.f64 y x) (if (<=.f64 z 150000000000000006280438121901244716806881918647697326742848129600338295293886572875743232) (+.f64 (.f64 z x) x) (if (<=.f64 z 74000000000000003292675868419441773450016658715608051850259778035325822929243804117411062511706674173316427036527874854277988879865182730538943771372700057993216) (.f64 z y) (.f64 z x)))))
(if (<=.f64 z -4307444211034609/281474976710656) (+.f64 x (.f64 z x)) (if (<=.f64 z 2052694448908761/37778931862957161709568) (+.f64 y x) (if (<=.f64 z 150000000000000006280438121901244716806881918647697326742848129600338295293886572875743232) (+.f64 x (.f64 z x)) (if (<=.f64 z 74000000000000003292675868419441773450016658715608051850259778035325822929243804117411062511706674173316427036527874854277988879865182730538943771372700057993216) (.f64 z y) (.f64 z x)))))
(if (<=.f64 z -4307444211034609/281474976710656) (.f64 z x) (if (<=.f64 z 4323308021388271/16) (+.f64 y x) (if (<=.f64 z 150000000000000006280438121901244716806881918647697326742848129600338295293886572875743232) (.f64 z x) (if (<=.f64 z 74000000000000003292675868419441773450016658715608051850259778035325822929243804117411062511706674173316427036527874854277988879865182730538943771372700057993216) (.f64 z y) (.f64 z x)))))
(if (<=.f64 x -5975658112521703) x (if (<=.f64 x -6382813411925257/174224571863520493293247799005065324265472) (.f64 z x) (if (<=.f64 x -7777572985336443/6129982163463555433433388108601236734474956488734408704) x (if (<=.f64 x -6983335091520329/97554642197374757230674913431036447054643691958280348464348654988292866838117675628759565720734124098744591597543956965482749239977758915821568) (.f64 z x) (if (<=.f64 x -386945396624257/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568) x (if (<=.f64 x -190901022513733/223741436863085634409521749481834675708763587282583222886261325799305187541819563744885033326754909183041871165773435313081225474664635755472226765949723278285256830531087594548959384855304521689414375064310509745905707450052637371994990524269330432) y (if (<=.f64 x -35091490030787/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912) (.f64 z y) (if (<=.f64 x 1643575090803453/251910462920982955146951572855242064723418868082104455055218081010186148908960752236565235084370225856148908135059894885483907489539473312974233140212507046179002134322645704349866637075627537275802723363977045251916898867011814946574400376685636747593659677933568) y (if (<=.f64 x 7249849670368581/328758493846773344202561867680008041596896237676448366218642556441795759643567551382104158517349278201686435553511138607063714515636487741445488423165742553122201479445527787386978984867770169829455828233486336) (.f64 z y) y)))))))))
(if (<=.f64 y 4985637244835055/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776) x (if (<=.f64 y 24343447907199218469252872089856837939759052555812864) (*.f64 z y) y))
(if (<=.f64 x -386945396624257/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568) x y)
x

Compiler

Compiled 232 to 130 computations (44% saved)

soundness0.0ms (0%)

end182.0ms (3.7%)

Remove: (sort x y)
Compiler: Compiled 233 to 111 computations (52.4% saved)

Details

analyze195.0ms (3.9%)

sample1.9s (37.6%)

preprocess78.0ms (1.6%)

simplify20.0ms (0.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize93.0ms (1.9%)

series11.0ms (0.2%)

rewrite150.0ms (3%)

simplify24.0ms (0.5%)

eval19.0ms (0.4%)

prune44.0ms (0.9%)

localize14.0ms (0.3%)

series5.0ms (0.1%)

rewrite54.0ms (1.1%)

simplify14.0ms (0.3%)

localize3.0ms (0.1%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite57.0ms (1.1%)

simplify9.0ms (0.2%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite56.0ms (1.1%)

simplify18.0ms (0.4%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite47.0ms (1%)

simplify10.0ms (0.2%)

eval160.0ms (3.2%)

prune25.0ms (0.5%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

series77.0ms (1.6%)

rewrite47.0ms (0.9%)

simplify16.0ms (0.3%)

localize9.0ms (0.2%)

series5.0ms (0.1%)

rewrite53.0ms (1.1%)

simplify50.0ms (1%)

eval49.0ms (1%)

prune17.0ms (0.3%)

eval10.0ms (0.2%)

prune4.0ms (0.1%)

regimes126.0ms (2.5%)

regimes90.0ms (1.8%)

regimes132.0ms (2.7%)

bsearch69.0ms (1.4%)

regimes120.0ms (2.4%)

bsearch54.0ms (1.1%)

regimes86.0ms (1.7%)

bsearch92.0ms (1.9%)

regimes99.0ms (2%)

bsearch86.0ms (1.7%)

regimes120.0ms (2.4%)

bsearch155.0ms (3.1%)

regimes68.0ms (1.4%)

bsearch40.0ms (0.8%)

regimes40.0ms (0.8%)

bsearch17.0ms (0.4%)

regimes12.0ms (0.2%)

simplify13.0ms (0.3%)

soundness0.0ms (0%)

end182.0ms (3.7%)

Profiling