Details

analyze186.0ms (5%)

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
25%	71.8%	3.3%	9
34.3%	60.1%	5.6%	10
41.3%	51.5%	7.2%	11
46.8%	44.1%	9.1%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample985.0ms (26.7%)

Results

850.0ms	8256×	body	256	valid
119.0ms	1191×	body	256	invalid

preprocess98.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

768×	`fma-neg_binary64`
441×	`fma-def_binary64`
180×	`cancel-sign-sub-inv_binary64`
127×	`distribute-rgt-in_binary64`
113×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	44
1	44	44
2	88	44
3	152	44
4	338	36
5	681	32
6	1139	32
7	1866	32
8	2487	32
9	2785	32
10	2860	32
11	2861	32
12	2861	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 (.f64 (-.f64 1 x) y) (.f64 x z))
(+.f64 (.f64 (-.f64 1 y) x) (.f64 y z))
(+.f64 (.f64 (-.f64 1 z) y) (.f64 z x))
(+.f64 (.f64 (-.f64 1 x) z) (.f64 x y))

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

346×	`fma-def_binary64`
246×	`fma-neg_binary64`
51×	`cancel-sign-sub-inv_binary64`
45×	`distribute-rgt-in_binary64`
42×	`associate--r+_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	17	11
2	30	11
3	57	11
4	126	9
5	218	8
6	346	8
7	557	8
8	961	8
9	1141	8
10	1201	8
11	1211	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 18 to 10 computations (44.4% saved)

prune1.0ms (0%)

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

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
▶	0.0b	(fma.f64 x (-.f64 z y) y)

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 14 computations (48.1% saved)

series7.0ms (0.2%)

Counts

2 → 60

Calls

15 calls:

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

rewrite78.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
411×	`prod-exp_binary64`
382×	`fma-def_binary64`
353×	`exp-prod_binary64`
343×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	192	18
2	2622	18

Stop Event

1×	node limit

Counts

2 → 122

Calls

Call 1

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

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

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

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

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

325×	`fma-def_binary64`
263×	`fma-neg_binary64`
69×	`cancel-sign-sub-inv_binary64`
53×	`distribute-rgt-in_binary64`
47×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	482
1	51	424
2	105	424
3	219	424
4	511	424
5	846	424
6	1139	424
7	1315	424
8	1331	424

Stop Event

1×

saturated

Counts

182 → 136

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 5 computations (66.7% saved)

series4.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

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

rewrite58.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`pow1_binary64`
686×	`add-log-exp_binary64`
686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
670×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1797	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

422×	`fma-def_binary64`
271×	`fma-neg_binary64`
63×	`distribute-rgt-in_binary64`
42×	`unsub-neg_binary64`
40×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	270
1	60	264
2	116	264
3	230	264
4	403	264
5	771	264
6	1141	264
7	1370	264
8	1380	264

Stop Event

1×

saturated

Counts

57 → 33

Calls

Call 1

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

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

eval43.0ms (1.2%)

Compiler: Compiled 2286 to 1166 computations (49% saved)

prune30.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (*.f64 (-.f64 z y) x) y)
▶	22.6b	(*.f64 y (-.f64 1 x))
	29.8b	(+.f64 (.f64 y (neg.f64 x)) (.f64 x z))
	32.9b	y
▶	40.2b	(*.f64 z x)
▶	22.6b	(-.f64 y (*.f64 y x))
▶	29.8b	(*.f64 (-.f64 z y) x)

Compiler

Compiled 106 to 69 computations (34.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 6 computations (71.4% saved)

series7.0ms (0.2%)

Counts

2 → 51

Calls

18 calls:

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

rewrite72.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

951×	`pow1_binary64`
883×	`add-log-exp_binary64`
883×	`log1p-expm1-u_binary64`
883×	`expm1-log1p-u_binary64`
864×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	159	15
2	2348	15

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
271×	`fma-neg_binary64`
62×	`distribute-rgt-in_binary64`
42×	`unsub-neg_binary64`
40×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	444
1	60	384
2	120	348
3	228	348
4	401	348
5	767	348
6	1144	348
7	1373	348
8	1383	348

Stop Event

1×

saturated

Counts

103 → 67

Calls

Call 1

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

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

localize3.0ms (0.1%)

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

localize10.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

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

rewrite77.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`pow1_binary64`
572×	`add-log-exp_binary64`
572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
561×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	122	7
2	1510	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

Outputs

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

simplify37.0ms (1%)

Algorithm

1×	egg-herbie

Rules

133×	`fma-def_binary64`
90×	`fma-neg_binary64`
22×	`cancel-sign-sub-inv_binary64`
21×	`associate-r_binary64`
17×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	94
1	13	76
2	30	76
3	46	76
4	64	76
5	128	76
6	253	76
7	359	76
8	457	76
9	533	76

Stop Event

1×

saturated

Counts

29 → 22

Calls

Call 1

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

Outputs
y
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))
(+.f64 y (.f64 -1 (.f64 y x)))
(+.f64 y (neg.f64 (*.f64 y x)))
(-.f64 y (*.f64 y x))
(fma.f64 y (neg.f64 x) y)
(*.f64 y (-.f64 1 x))

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 5 computations (64.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 5 computations (61.5% saved)

series5.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

649×	`pow1_binary64`
604×	`add-log-exp_binary64`
604×	`log1p-expm1-u_binary64`
604×	`expm1-log1p-u_binary64`
591×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	113	7
2	1650	7

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

124×	`fma-def_binary64`
69×	`fma-neg_binary64`
20×	`cancel-sign-sub-inv_binary64`
18×	`associate-r_binary64`
18×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	160
1	33	160
2	51	160
3	88	160
4	122	160
5	201	160
6	341	160
7	419	160
8	489	160
9	495	160

Stop Event

1×

saturated

Counts

62 → 44

Calls

Call 1

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

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

eval97.0ms (2.6%)

Compiler: Compiled 1693 to 560 computations (66.9% saved)

prune151.0ms (4.1%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	2	0	2
Picked	0	1	1
Done	0	4	4
Total	152	8	160

Error

Counts

160 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.9b	y
✓	22.6b	(*.f64 y (-.f64 1 x))
✓	0.0b	(+.f64 (*.f64 (-.f64 z y) x) y)
✓	22.6b	(-.f64 y (*.f64 y x))
▶	52.3b	(*.f64 y (neg.f64 x))
✓	29.8b	(*.f64 (-.f64 z y) x)
▶	29.8b	(+.f64 (.f64 z x) (.f64 (neg.f64 y) x))
✓	40.2b	(*.f64 z x)

Compiler

Compiled 62 to 41 computations (33.9% saved)

localize9.0ms (0.2%)

Compiler: Compiled 11 to 5 computations (54.5% saved)

localize42.0ms (1.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 23 to 7 computations (69.6% saved)

series6.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

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

rewrite156.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`pow1_binary64`
773×	`add-log-exp_binary64`
772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
756×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	176	7
2	2563	7

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

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

Outputs

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

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

168×	`fma-def_binary64`
110×	`fma-neg_binary64`
38×	`unsub-neg_binary64`
35×	`cancel-sign-sub-inv_binary64`
29×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	330
1	36	240
2	80	240
3	159	240
4	322	240
5	487	240
6	655	240
7	728	240
8	730	240

Stop Event

1×

saturated

Counts

80 → 52

Calls

Call 1

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

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

eval18.0ms (0.5%)

Compiler: Compiled 610 to 201 computations (67% saved)

prune12.0ms (0.3%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	1	1
Picked	1	0	1
Done	0	6	6
Total	52	8	60

Error

Counts

60 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.9b	y
✓	22.6b	(*.f64 y (-.f64 1 x))
✓	0.0b	(+.f64 (*.f64 (-.f64 z y) x) y)
✓	22.6b	(-.f64 y (*.f64 y x))
✓	52.3b	(*.f64 y (neg.f64 x))
▶	29.8b	(-.f64 (.f64 z x) (.f64 x y))
✓	40.2b	(*.f64 z x)
✓	29.8b	(*.f64 (-.f64 z y) x)

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 6 computations (68.4% saved)

series3.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

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

rewrite68.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`pow1_binary64`
812×	`add-log-exp_binary64`
812×	`log1p-expm1-u_binary64`
812×	`expm1-log1p-u_binary64`
795×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	160	7
2	2222	7

Stop Event

1×	node limit

Counts

1 → 49

Calls

Call 1

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

Outputs

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

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

129×	`fma-def_binary64`
70×	`fma-neg_binary64`
37×	`unsub-neg_binary64`
29×	`distribute-rgt-in_binary64`
28×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	330
1	43	240
2	99	240
3	261	240
4	439	240
5	557	240
6	626	240
7	631	240

Stop Event

1×

saturated

Counts

85 → 56

Calls

Call 1

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

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

eval11.0ms (0.3%)

Compiler: Compiled 820 to 203 computations (75.2% saved)

prune12.0ms (0.3%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	56	8	64

Error

Counts

64 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.9b	y
✓	22.6b	(*.f64 y (-.f64 1 x))
✓	0.0b	(+.f64 (*.f64 (-.f64 z y) x) y)
✓	22.6b	(-.f64 y (*.f64 y x))
✓	52.3b	(*.f64 y (neg.f64 x))
✓	29.8b	(-.f64 (.f64 z x) (.f64 x y))
✓	40.2b	(*.f64 z x)
✓	29.8b	(*.f64 (-.f64 z y) x)

Compiler

Compiled 61 to 40 computations (34.4% saved)

regimes153.0ms (4.1%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

67.0ms	x
25.0ms	z
16.0ms	y
8.0ms	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))

Results

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

Compiler

Compiled 96 to 43 computations (55.2% saved)

regimes44.0ms (1.2%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

4 calls:

18.0ms	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
7.0ms	y
7.0ms	z
7.0ms	x

Results

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

Compiler

Compiled 90 to 42 computations (53.3% saved)

regimes55.0ms (1.5%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

39.0ms	x
7.0ms	y
7.0ms	z

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`z`

Compiler

Compiled 69 to 30 computations (56.5% saved)

regimes131.0ms (3.5%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

3 calls:

54.0ms	z
44.0ms	x
30.0ms	y

Results

Error	Segments	Branch
9.6b	3	`x`
11.1b	5	`y`
13.0b	5	`z`

Compiler

Compiled 46 to 24 computations (47.8% saved)

bsearch52.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
35.0ms	1760.9916923675491	1123298257418.2163
17.0ms	-2.559896827918228e-35	-1.439588685551652e-38

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes61.0ms (1.7%)

Counts

6 → 5

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	y
21.0ms	z
13.0ms	x

Results

Error	Segments	Branch
19.3b	3	`x`
13.0b	5	`y`
13.7b	5	`z`

Compiler

Compiled 34 to 20 computations (41.2% saved)

bsearch91.0ms (2.5%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
42.0ms	8.677424855452824e-132	1.1543949311235875e-126
16.0ms	-4.589904501399187e-173	-1.0702466985588288e-180
17.0ms	-7.663830166888013e-23	-6.066430808983345e-27
16.0ms	-5.279637595719111e+47	-2.486568160162605e+46

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes58.0ms (1.6%)

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	y
20.0ms	z
12.0ms	x

Results

Error	Segments	Branch
19.3b	3	`x`
13.0b	5	`y`
13.7b	5	`z`

Compiler

Compiled 29 to 18 computations (37.9% saved)

bsearch105.0ms (2.8%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
17.0ms	8.677424855452824e-132	1.1543949311235875e-126
54.0ms	-4.589904501399187e-173	-1.0702466985588288e-180
17.0ms	-7.663830166888013e-23	-6.066430808983345e-27
17.0ms	-5.279637595719111e+47	-2.486568160162605e+46

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes66.0ms (1.8%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

28.0ms	y
26.0ms	z
11.0ms	x

Results

Error	Segments	Branch
20.1b	3	`x`
20.2b	7	`y`
22.2b	7	`z`

Compiler

Compiled 24 to 15 computations (37.5% saved)

bsearch33.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	2.4899264046478662e-17	8.520736511456776e-16
17.0ms	-2.559896827918228e-35	-1.439588685551652e-38

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes10.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
y
y

Outputs
y

Calls

3 calls:

3.0ms	y
3.0ms	x
3.0ms	z

Results

Error	Segments	Branch
32.9b	1	`x`
32.9b	1	`y`
32.9b	1	`z`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	192
1	56	192
2	70	192
3	76	192
4	79	192

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x (-.f64 z y) y)
(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
(+.f64 (*.f64 (-.f64 z y) x) y)
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 (-.f64 z y) x) (if (<=.f64 x 1936230842175057/1099511627776) (.f64 y (-.f64 1 x)) (*.f64 (-.f64 z y) x)))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (-.f64 y (.f64 y x)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 z x) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 z x) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (.f64 y (-.f64 1 x)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 z x) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 z x) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 z x) (if (<=.f64 x 8080273155522521/324518553658426726783156020576256) y (.f64 z x)))
y

Outputs
(fma.f64 x (-.f64 z y) y)
(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
(+.f64 (.f64 y (-.f64 1 x)) (.f64 x z))
(+.f64 (*.f64 (-.f64 z y) x) y)
(+.f64 y (*.f64 x (-.f64 z y)))
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 (-.f64 z y) x) (if (<=.f64 x 1936230842175057/1099511627776) (.f64 y (-.f64 1 x)) (*.f64 (-.f64 z y) x)))
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 x (-.f64 z y)) (if (<=.f64 x 1936230842175057/1099511627776) (.f64 y (-.f64 1 x)) (*.f64 x (-.f64 z y))))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (-.f64 y (.f64 y x)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 z x) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 z x) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (-.f64 y (.f64 x y)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 x z) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 x z) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (.f64 y (-.f64 1 x)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 z x) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 z x) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 y -527963759571911106819329749561442987046634258432) (.f64 y (-.f64 1 x)) (if (<=.f64 y -1629916418042965/21267647932558653966460912964485513216) (.f64 x z) (if (<=.f64 y -6390736916562073/139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432) (.f64 y (-.f64 1 x)) (if (<=.f64 y 433419815407773/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (.f64 x z) (*.f64 y (-.f64 1 x))))))
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 z x) (if (<=.f64 x 8080273155522521/324518553658426726783156020576256) y (.f64 z x)))
(if (<=.f64 x -149651736216027/5846006549323611672814739330865132078623730171904) (.f64 x z) (if (<=.f64 x 8080273155522521/324518553658426726783156020576256) y (.f64 x z)))
y

Compiler

Compiled 159 to 95 computations (40.3% saved)

soundness80.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

346×	`fma-def_binary64`
246×	`fma-neg_binary64`
51×	`cancel-sign-sub-inv_binary64`
45×	`distribute-rgt-in_binary64`
42×	`associate--r+_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	17	11
2	30	11
3	57	11
4	126	9
5	218	8
6	346	8
7	557	8
8	961	8
9	1141	8
10	1201	8
11	1211	8

Stop Event

1×

saturated

Compiler

Compiled 197 to 126 computations (36% saved)

end69.0ms (1.9%)

Compiler: Compiled 138 to 68 computations (50.7% saved)

Iter	Nodes	Cost
0	13	160
1	33	160
2	51	160
3	88	160
4	122	160
5	201	160
6	341	160
7	419	160
8	489	160
9	495	160

Iter	Nodes	Cost
0	16	330
1	36	240
2	80	240
3	159	240
4	322	240
5	487	240
6	655	240
7	728	240
8	730	240

Iter	Nodes	Cost
0	13	160
1	33	160
2	51	160
3	88	160
4	122	160
5	201	160
6	341	160
7	419	160
8	489	160
9	495	160

Iter	Nodes	Cost
0	16	330
1	36	240
2	80	240
3	159	240
4	322	240
5	487	240
6	655	240
7	728	240
8	730	240

Details

analyze186.0ms (5%)

sample985.0ms (26.7%)

preprocess98.0ms (2.7%)

simplify34.0ms (0.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.3%)

series7.0ms (0.2%)

rewrite78.0ms (2.1%)

simplify51.0ms (1.4%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite58.0ms (1.6%)

simplify42.0ms (1.1%)

eval43.0ms (1.2%)

prune30.0ms (0.8%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite72.0ms (2%)

simplify49.0ms (1.3%)

localize3.0ms (0.1%)

localize10.0ms (0.3%)

series3.0ms (0.1%)

rewrite77.0ms (2.1%)

simplify37.0ms (1%)

localize7.0ms (0.2%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite52.0ms (1.4%)

simplify30.0ms (0.8%)

eval97.0ms (2.6%)

prune151.0ms (4.1%)

localize9.0ms (0.2%)

localize42.0ms (1.1%)

series6.0ms (0.2%)

rewrite156.0ms (4.2%)

simplify47.0ms (1.3%)

eval18.0ms (0.5%)

prune12.0ms (0.3%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite68.0ms (1.9%)

simplify30.0ms (0.8%)

eval11.0ms (0.3%)

prune12.0ms (0.3%)

regimes153.0ms (4.1%)

regimes44.0ms (1.2%)

regimes55.0ms (1.5%)

regimes131.0ms (3.5%)

bsearch52.0ms (1.4%)

regimes61.0ms (1.7%)

bsearch91.0ms (2.5%)

regimes58.0ms (1.6%)

bsearch105.0ms (2.8%)

regimes66.0ms (1.8%)

bsearch33.0ms (0.9%)

regimes10.0ms (0.3%)

simplify14.0ms (0.4%)

soundness80.0ms (2.2%)

end69.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	13	160
1	33	160
2	51	160
3	88	160
4	122	160
5	201	160
6	341	160
7	419	160
8	489	160
9	495	160

Iter	Nodes	Cost
0	16	330
1	36	240
2	80	240
3	159	240
4	322	240
5	487	240
6	655	240
7	728	240
8	730	240