Details

analyze369.0ms (25.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
34.3%	63.2%	2.5%	9
40.6%	52.7%	6.8%	10
48.4%	42.1%	9.5%	11
56.2%	32.5%	11.4%	12
59.1%	26.9%	14%	13
63.9%	21%	15.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample816.0ms (55.6%)

Results

751.0ms	8256×	body	128	valid
52.0ms	596×	body	128	invalid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess23.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

188×	`fma-def_binary64`
26×	`+-commutative_binary64`
22×	`distribute-rgt-in_binary64`
18×	`*-commutative_binary64`
16×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	42	32
2	130	32
3	183	32
4	202	32
5	228	32
6	252	32
7	324	32
8	397	32
9	416	32
10	420	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

simplify8.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-def_binary64`
8×	`+-commutative_binary64`
8×	`associate-r_binary64`
8×	`associate-l_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	8
2	35	8
3	50	8
4	59	8
5	66	8
6	72	8
7	91	8
8	107	8
9	121	8
10	139	8
11	146	8
12	147	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune2.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize7.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.8%)

Counts

2 → 60

Calls

18 calls:

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

rewrite47.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`fma-def_binary64`
429×	`log-prod_binary64`
202×	`fma-neg_binary64`
156×	`expm1-udef_binary64`
156×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	163	15
2	2590	15

Stop Event

1×	node limit

Counts

2 → 127

Calls

Call 1

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

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

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

simplify28.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-def_binary64`
8×	`associate-r_binary64`
8×	`associate-l_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	435
1	35	408
2	52	408
3	62	408
4	81	408
5	97	408
6	111	408
7	129	408
8	136	408
9	137	408

Stop Event

1×

saturated

Counts

187 → 137

Calls

Call 1

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

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

prune59.0ms (4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	1	139

Error

Counts

139 → 1

Alt Table

Status	Error	Program
▶	0b	(fma.f64 y z (fma.f64 y x x))

Compiler

Compiled 1769 to 486 computations (72.5% saved)

localize4.0ms (0.3%)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Status	Error	Program
✓	0b	(fma.f64 y z (fma.f64 y x x))

Compiler

Compiled 10 to 5 computations (50% saved)

regimes61.0ms (4.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

16 → 1

Compiler

Compiled 620 to 378 computations (39% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9

Stop Event

1×

saturated

Calls

Call 1

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

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

end30.0ms (2.1%)

Stop Event

1×

done

Compiler

Compiled 30 to 15 computations (50% saved)

Iter	Nodes	Cost
0	16	40
1	42	32
2	130	32
3	183	32
4	202	32
5	228	32
6	252	32
7	324	32
8	397	32
9	416	32
10	420	32
0	3	3

Iter	Nodes	Cost
0	7	10
1	16	8
2	35	8
3	50	8
4	59	8
5	66	8
6	72	8
7	91	8
8	107	8
9	121	8
10	139	8
11	146	8
12	147	8

Iter	Nodes	Cost
0	15	435
1	35	408
2	52	408
3	62	408
4	81	408
5	97	408
6	111	408
7	129	408
8	136	408
9	137	408

Iter	Nodes	Cost
0	16	40
1	42	32
2	130	32
3	183	32
4	202	32
5	228	32
6	252	32
7	324	32
8	397	32
9	416	32
10	420	32
0	3	3

Iter	Nodes	Cost
0	7	10
1	16	8
2	35	8
3	50	8
4	59	8
5	66	8
6	72	8
7	91	8
8	107	8
9	121	8
10	139	8
11	146	8
12	147	8

Iter	Nodes	Cost
0	15	435
1	35	408
2	52	408
3	62	408
4	81	408
5	97	408
6	111	408
7	129	408
8	136	408
9	137	408

Details

analyze369.0ms (25.1%)

sample816.0ms (55.6%)

preprocess23.0ms (1.6%)

simplify8.0ms (0.6%)

prune2.0ms (0.2%)

localize7.0ms (0.5%)

series12.0ms (0.8%)

rewrite47.0ms (3.2%)

simplify28.0ms (1.9%)

prune59.0ms (4%)

localize4.0ms (0.3%)

prune1.0ms (0%)

regimes61.0ms (4.1%)

simplify2.0ms (0.1%)

end30.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	16	40
1	42	32
2	130	32
3	183	32
4	202	32
5	228	32
6	252	32
7	324	32
8	397	32
9	416	32
10	420	32
0	3	3

Iter	Nodes	Cost
0	7	10
1	16	8
2	35	8
3	50	8
4	59	8
5	66	8
6	72	8
7	91	8
8	107	8
9	121	8
10	139	8
11	146	8
12	147	8

Iter	Nodes	Cost
0	15	435
1	35	408
2	52	408
3	62	408
4	81	408
5	97	408
6	111	408
7	129	408
8	136	408
9	137	408