Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample836.0ms (34.3%)

Results

826.0ms

8256×

body

256

valid

preprocess19.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	23	20
2	43	20
3	79	20
4	122	20
5	152	20
6	172	20
7	189	20
8	191	20
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 (+.f64 b a) (+.f64 b a))

Outputs
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 (+.f64 b a) (+.f64 b a))
(*.f64 (+.f64 a b) (+.f64 a b))

Symmetry

(sort a b)

Compiler

Compiled 11 to 6 computations (45.5% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	29	10
3	67	10
4	110	10
5	140	10
6	160	10
7	177	10
8	179	10

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (+.f64 a b) (+.f64 a b))

Outputs
(*.f64 (+.f64 a b) (+.f64 a b))

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))

Compiler

Compiled 9 to 4 computations (55.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 4 computations (71.4% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	(*.f64 (+.f64 a b) (+.f64 a b))
0.0ms	a	@	-inf	(*.f64 (+.f64 a b) (+.f64 a b))
0.0ms	a	@	inf	(*.f64 (+.f64 a b) (+.f64 a b))
0.0ms	b	@	inf	(*.f64 (+.f64 a b) (+.f64 a b))
0.0ms	b	@	-inf	(*.f64 (+.f64 a b) (+.f64 a b))

rewrite41.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`pow1_binary64`
618×	`add-log-exp_binary64`
618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
600×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1743	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(*.f64 (+.f64 a b) (+.f64 a b))

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

Outputs

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

simplify154.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
615×	`fma-def_binary64`
606×	`cube-prod_binary64`
548×	`fabs-mul_binary64`
372×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	294
1	32	267
2	69	222
3	151	216
4	414	216
5	1500	216
6	2773	216
7	3045	216
8	3230	216
9	3474	216
10	3777	216
11	4170	216
12	4679	216
13	5257	216
14	5999	216
15	6549	216
16	6883	216
17	7203	216
18	7285	216
19	7315	216
20	7966	216

Stop Event

1×	node limit

Counts

50 → 36

Calls

Call 1

Inputs
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))

Outputs
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 b a) (.f64 b b))
(.f64 b (+.f64 b (.f64 2 a)))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 b a) (.f64 a a))
(.f64 a (+.f64 (.f64 b 2) a))
(*.f64 a (fma.f64 b 2 a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 b a) (.f64 a a))
(.f64 a (+.f64 (.f64 b 2) a))
(*.f64 a (fma.f64 b 2 a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 b a) (.f64 a a))
(.f64 a (+.f64 (.f64 b 2) a))
(*.f64 a (fma.f64 b 2 a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 b a) (.f64 b b))
(.f64 b (+.f64 b (.f64 2 a)))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 b a) (.f64 b b))
(.f64 b (+.f64 b (.f64 2 a)))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 b a) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 b a) (fma.f64 b b (.f64 a a)))
(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
(fma.f64 b b (*.f64 a (fma.f64 b 2 a)))

eval7.0ms (0.3%)

Compiler: Compiled 471 to 165 computations (65% saved)

prune7.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Error

Counts

37 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.7b	(*.f64 b b)
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
▶	0.0b	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
▶	0.0b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 35 to 18 computations (48.6% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 15 to 8 computations (46.7% saved)

series4.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	(*.f64 b (fma.f64 2 a b))
1.0ms	b	@	0	(*.f64 b (fma.f64 2 a b))
1.0ms	b	@	-inf	(*.f64 b (fma.f64 2 a b))
1.0ms	a	@	-inf	(*.f64 b (fma.f64 2 a b))
1.0ms	b	@	inf	(*.f64 b (fma.f64 2 a b))

rewrite39.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
531×	`add-sqr-sqrt_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1364	8

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 b (fma.f64 2 a b))

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

Outputs

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

simplify160.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

801×	`sqr-pow_binary64`
582×	`fma-def_binary64`
565×	`cube-prod_binary64`
560×	`fabs-mul_binary64`
541×	`pow-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	213
2	41	177
3	79	177
4	167	177
5	469	177
6	1554	177
7	2782	177
8	3129	177
9	3351	177
10	3573	177
11	3879	177
12	4301	177
13	4791	177
14	5360	177
15	6056	177
16	6906	177
17	7301	177
18	7589	177
19	7865	177
20	7935	177
21	7971	177

Stop Event

1×	node limit

Counts

37 → 19

Calls

Call 1

Inputs
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))

Outputs
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 6 computations (78.6% saved)

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	b	@	inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
0.0ms	b	@	0	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
0.0ms	b	@	-inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
0.0ms	a	@	0	(*.f64 a (+.f64 a b))
0.0ms	a	@	inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))

rewrite164.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`fma-def_binary64`
482×	`prod-exp_binary64`
428×	`log-prod_binary64`
398×	`pow-prod-down_binary64`
299×	`exp-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	167	14
2	2610	14

Stop Event

1×	node limit

Counts

2 → 174

Calls

Call 1

Inputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(*.f64 a (+.f64 a b))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 b a) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 b (+.f64 b a)) 2) (*.f64 (+.f64 b a) (-.f64 b a))) (/.f64 (pow.f64 (*.f64 a (+.f64 b a)) 2) (*.f64 (+.f64 b a) (-.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 b a) (+.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 b a) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 b a) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 b a)) 2) (pow.f64 (cbrt.f64 (+.f64 b a)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 b a)) 4) (pow.f64 (cbrt.f64 (+.f64 b a)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 b a)) (pow.f64 (+.f64 b a) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3)) (/.f64 1 (fma.f64 (*.f64 a (+.f64 b a)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))) (pow.f64 (*.f64 b (+.f64 b a)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 b a) 2) (*.f64 (+.f64 b a) (-.f64 b a))) (/.f64 1 (*.f64 (+.f64 b a) (-.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 b a) 3/2) (sqrt.f64 (+.f64 b a)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 b a)) 5) (cbrt.f64 (+.f64 b a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 a (+.f64 b a)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))) (pow.f64 (*.f64 b (+.f64 b a)) 2)) (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 (pow.f64 (+.f64 b a) 2) (*.f64 (+.f64 b a) (-.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3)) (fma.f64 (*.f64 a (+.f64 b a)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))) (pow.f64 (*.f64 b (+.f64 b a)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3)) (+.f64 (pow.f64 (*.f64 a (+.f64 b a)) 2) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) 2) (*.f64 b (*.f64 (+.f64 b a) (*.f64 a (+.f64 b a)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (+.f64 b a) 2) (*.f64 (+.f64 b a) (-.f64 b a))) (*.f64 (+.f64 b a) (-.f64 b a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (-.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (-.f64 a b) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) 2) (pow.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3))) (neg.f64 (fma.f64 (*.f64 a (+.f64 b a)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))) (pow.f64 (*.f64 b (+.f64 b a)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 (+.f64 b a) 2) (*.f64 (+.f64 b a) (-.f64 b a)))) (neg.f64 (*.f64 (+.f64 b a) (-.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (+.f64 (pow.f64 a 3) (pow.f64 b 3))) (*.f64 (-.f64 a b) (fma.f64 b (-.f64 b a) (*.f64 a a))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (-.f64 (*.f64 a a) (*.f64 b b))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (-.f64 a b)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 a (+.f64 b a)) 2) (pow.f64 (*.f64 b (+.f64 b a)) 2)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 b a)) (fma.f64 b (-.f64 b a) (*.f64 a a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (+.f64 b a)) (-.f64 a b))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 b a) (+.f64 (pow.f64 a 3) (pow.f64 b 3))) (fma.f64 b (-.f64 b a) (*.f64 a a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 b a) (-.f64 (*.f64 a a) (*.f64 b b))) (-.f64 a b))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 b a) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 b a) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 b a) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 b a) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 b a) 3) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (+.f64 b a)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 b a)) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 b a)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (*.f64 2 (log.f64 (+.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 a (+.f64 b a)) (-.f64 (*.f64 a (+.f64 b a)) (*.f64 b (+.f64 b a))) (pow.f64 (*.f64 b (+.f64 b a)) 2)) (+.f64 (pow.f64 (*.f64 b (+.f64 b a)) 3) (pow.f64 (*.f64 a (+.f64 b a)) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 (pow.f64 (+.f64 b a) 2) (*.f64 (+.f64 b a) (-.f64 b a)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 2 (log.f64 (+.f64 b a)))) 2)) (cbrt.f64 (*.f64 2 (log.f64 (+.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 2 (log.f64 (+.f64 b a))))) (sqrt.f64 (*.f64 2 (log.f64 (+.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 b a) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 b a) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 b a) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 b (+.f64 b a)))) (pow.f64 (exp.f64 a) (+.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 b) (+.f64 b a)) (+.f64 1 (expm1.f64 (*.f64 a (+.f64 b a))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 b (+.f64 b a)))) (+.f64 1 (expm1.f64 (*.f64 a (+.f64 b a))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 a (+.f64 b a)))) (pow.f64 (exp.f64 b) (+.f64 b a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 a) (+.f64 b a)) (+.f64 1 (expm1.f64 (*.f64 b (+.f64 b a))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 a (+.f64 b a)))) (+.f64 1 (expm1.f64 (*.f64 b (+.f64 b a))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 b a) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a a) (*.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 b a) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 a (+.f64 b a)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a a) 1) (*.f64 (*.f64 b a) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 a) (+.f64 b a))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 a) (+.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a) (+.f64 b a)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a) (+.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a (+.f64 b a)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a 6) (pow.f64 (*.f64 b a) 3)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 (*.f64 b a) 2) (*.f64 (*.f64 a a) (*.f64 b a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a 4) 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(*.f64 (cbrt.f64 b) a) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a) (pow.f64 a 3/2) (*.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a) (*.f64 (sqrt.f64 a) b) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 b) (*.f64 (sqrt.f64 b) a) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 a 3/2) (sqrt.f64 a) (*.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 a) a) (pow.f64 (cbrt.f64 a) 2) (*.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 b a)) 2) (cbrt.f64 (*.f64 b a)) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 b a)) (sqrt.f64 (*.f64 b a)) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 b (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 b (sqrt.f64 a)) (sqrt.f64 a) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a) 5) (cbrt.f64 a) (*.f64 b a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a (pow.f64 (cbrt.f64 b) 2)) (cbrt.f64 b) (*.f64 a a))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a (sqrt.f64 b)) (sqrt.f64 b) (*.f64 a a))))))

simplify275.0ms (11.3%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
826×	`fma-def_binary64`
566×	`fabs-mul_binary64`
537×	`cube-prod_binary64`
392×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	462
1	35	417
2	79	372
3	169	366
4	459	366
5	1626	366
6	3051	366
7	3395	366
8	3587	366
9	3835	366
10	4137	366
11	4534	366
12	5045	366
13	5623	366
14	6377	366
15	6934	366
16	7272	366
17	7598	366
18	7686	366
19	7718	366

Stop Event

1×	node limit

Counts

222 → 187

Calls

Call 1

Inputs
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(pow.f64 a 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(+.f64 (*.f64 a b) (pow.f64 a 2))

Outputs
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 a b) (.f64 a a))
(fma.f64 a a (.f64 a (.f64 b 2)))
(.f64 a (+.f64 a (.f64 2 b)))
(*.f64 a (fma.f64 2 b a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 a 2) b))
(*.f64 b (fma.f64 a 2 b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 a 2) b))
(*.f64 b (fma.f64 a 2 b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 a 2) b))
(*.f64 b (fma.f64 a 2 b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 a b) (.f64 a a))
(fma.f64 a a (.f64 a (.f64 b 2)))
(.f64 a (+.f64 a (.f64 2 b)))
(*.f64 a (fma.f64 2 b a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 a 2))
(fma.f64 2 (.f64 a b) (.f64 a a))
(fma.f64 a a (.f64 a (.f64 b 2)))
(.f64 a (+.f64 a (.f64 2 b)))
(*.f64 a (fma.f64 2 b a))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 b 2) (pow.f64 a 2)))
(+.f64 (fma.f64 2 (.f64 a b) (.f64 b b)) (*.f64 a a))
(fma.f64 2 (.f64 a b) (fma.f64 a a (.f64 b b)))
(fma.f64 b (fma.f64 a 2 b) (*.f64 a a))
(fma.f64 a a (*.f64 b (fma.f64 a 2 b)))
(fma.f64 a (fma.f64 2 b a) (*.f64 b b))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(*.f64 a b)
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))
(+.f64 (*.f64 a b) (pow.f64 a 2))
(fma.f64 a b (*.f64 a a))
(*.f64 a (+.f64 a b))

eval186.0ms (7.6%)

Compiler: Compiled 3034 to 890 computations (70.7% saved)

prune54.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	207	3	210

Error

Counts

210 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(*.f64 b b)
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
▶	0.0b	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

Compiler

Compiled 25 to 13 computations (48% saved)

localize36.0ms (1.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

Compiler

Compiled 24 to 6 computations (75% saved)

series6.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	b	@	0	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))
1.0ms	b	@	inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))
1.0ms	b	@	-inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))
1.0ms	a	@	inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))
1.0ms	a	@	-inf	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

rewrite163.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

968×	`pow1_binary64`
902×	`add-log-exp_binary64`
902×	`log1p-expm1-u_binary64`
902×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	161	10
2	2453	10

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

Inputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

Outputs

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

simplify163.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

801×	`sqr-pow_binary64`
582×	`fma-def_binary64`
565×	`cube-prod_binary64`
560×	`fabs-mul_binary64`
541×	`pow-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	213
2	41	177
3	79	177
4	167	177
5	469	177
6	1554	177
7	2782	177
8	3129	177
9	3351	177
10	3573	177
11	3879	177
12	4301	177
13	4791	177
14	5360	177
15	6056	177
16	6906	177
17	7301	177
18	7589	177
19	7865	177
20	7935	177
21	7971	177

Stop Event

1×	node limit

Counts

64 → 46

Calls

Call 1

Inputs
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(pow.f64 b 2)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(.f64 2 (.f64 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))

Outputs
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(pow.f64 b 2)
(*.f64 b b)
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(.f64 2 (.f64 a b))
(.f64 b (.f64 2 a))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))
(+.f64 (.f64 2 (.f64 a b)) (pow.f64 b 2))
(fma.f64 2 (.f64 a b) (.f64 b b))
(.f64 b (+.f64 (.f64 2 a) b))
(*.f64 b (fma.f64 2 a b))

eval10.0ms (0.4%)

Compiler: Compiled 679 to 192 computations (71.7% saved)

prune7.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(*.f64 b b)
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
✓	0.0b	(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

Compiler

Compiled 25 to 13 computations (48% saved)

regimes21.0ms (0.9%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) (+.f64 a b))
(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(*.f64 b (fma.f64 2 a b))

Outputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))

Calls

4 calls:

6.0ms	b
5.0ms	(*.f64 (+.f64 a b) (+.f64 a b))
4.0ms	(+.f64 a b)
3.0ms	a

Results

Error	Segments	Branch
0.0b	1	`a`
0.0b	1	`b`
0.0b	1	`(*.f64 (+.f64 a b) (+.f64 a b))`
0.0b	1	`(+.f64 a b)`

Compiler

Compiled 58 to 24 computations (58.6% saved)

regimes20.0ms (0.8%)

Accuracy

Total -0.7b remaining (-6266.6%)

Threshold costs -0.7b (-6266.6%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) (+.f64 a b))
(+.f64 (.f64 b (+.f64 a b)) (.f64 a b))

Outputs
(*.f64 (+.f64 a b) (+.f64 a b))

Calls

4 calls:

6.0ms	(+.f64 a b)
5.0ms	a
4.0ms	(*.f64 (+.f64 a b) (+.f64 a b))
4.0ms	b

Results

Error	Segments	Branch
0.0b	1	`a`
0.0b	1	`b`
0.0b	1	`(*.f64 (+.f64 a b) (+.f64 a b))`
0.0b	1	`(+.f64 a b)`

Compiler

Compiled 41 to 19 computations (53.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	13	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 b b)

Outputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(+.f64 (.f64 b (+.f64 b a)) (.f64 a (+.f64 b a)))
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 (+.f64 b a) (+.f64 b a))
(*.f64 b b)

end22.0ms (0.9%)

Stop Event

1×

done

Remove

(sort a b)

Compiler

Compiled 76 to 33 computations (56.6% saved)

Details

analyze0.0ms (0%)

sample836.0ms (34.3%)

preprocess19.0ms (0.8%)

simplify10.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite41.0ms (1.7%)

simplify154.0ms (6.3%)

eval7.0ms (0.3%)

prune7.0ms (0.3%)

localize3.0ms (0.1%)

localize7.0ms (0.3%)

series4.0ms (0.2%)

rewrite39.0ms (1.6%)

simplify160.0ms (6.6%)

localize8.0ms (0.3%)

series5.0ms (0.2%)

rewrite164.0ms (6.7%)

simplify275.0ms (11.3%)

eval186.0ms (7.6%)

prune54.0ms (2.2%)

localize36.0ms (1.5%)

series6.0ms (0.2%)

rewrite163.0ms (6.7%)

simplify163.0ms (6.7%)

eval10.0ms (0.4%)

prune7.0ms (0.3%)

regimes21.0ms (0.9%)

regimes20.0ms (0.8%)

simplify2.0ms (0.1%)

end22.0ms (0.9%)

Profiling