Details

analyze100.0ms (2.2%)

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
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	43.7%	31.3%	7
31.2%	31.2%	37.6%	8
39%	23.4%	37.6%	9
42.9%	16.4%	40.7%	10
47.2%	12.1%	40.7%	11
49.4%	8.4%	42.2%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (33.1%)

Results

1.4s	8256×	body	256	valid
37.0ms	260×	body	256	invalid

preprocess20.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

26×	`fma-def_binary64`
11×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	22
2	62	22
3	76	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	34	11
3	42	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 21 to 11 computations (47.6% 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	(fma.f64 x (+.f64 x 2) (*.f64 y y))
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 23 to 14 computations (39.1% saved)

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 32 to 14 computations (56.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite71.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`pow1_binary64`
634×	`add-log-exp_binary64`
633×	`log1p-expm1-u_binary64`
633×	`expm1-log1p-u_binary64`
620×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	133	7
2	1784	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 x 2) (.f64 x x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 4) (.f64 x (-.f64 2 x))) (/.f64 (pow.f64 x 4) (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 (.f64 x 2))) (hypot.f64 x (sqrt.f64 (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 2 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (/.f64 1 (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 2 (pow.f64 x 3)))) (+.f64 (.f64 8 (pow.f64 x 3)) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x (-.f64 2 x)) (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (.f64 x (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 8 (pow.f64 x 3)) (pow.f64 x 6))) (neg.f64 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 2 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4))) (neg.f64 (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (-.f64 (.f64 x x) (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 2) (cbrt.f64 (.f64 x 2)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2)) (*.f64 x x))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 2 x))) (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) (hypot.f64 x (sqrt.f64 (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 2 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (/.f64 1 (*.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 2 (pow.f64 x 3)))) (+.f64 (*.f64 8 (pow.f64 x 3)) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 2 x)) (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 8 (pow.f64 x 3)) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (*.f64 x (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 8 (pow.f64 x 3)) (pow.f64 x 6))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 2 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4))) (neg.f64 (*.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (-.f64 (*.f64 x x) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))))))

simplify192.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

51 → 44

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize17.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 9 computations (52.6% saved)

series9.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	y	@	0	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	x	@	0	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	x	@	-inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	y	@	-inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))

rewrite116.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
690×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
675×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1860	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify198.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	262
1	34	214
2	59	214
3	87	214
4	192	214
5	511	214
6	1715	214
7	2370	214
8	2701	214
9	2961	214
10	3300	214
11	3806	214
12	4467	214
13	5261	214
14	6190	214
15	6711	214
16	7124	214
17	7517	214
18	7644	214
19	7690	214

Stop Event

1×	node limit

Counts

45 → 33

Calls

Call 1

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

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(*.f64 (+.f64 2 x) x)
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))

eval45.0ms (1%)

Compiler: Compiled 1040 to 579 computations (44.3% saved)

prune29.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Error

Counts

79 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	38.0b	(*.f64 y y)
▶	44.9b	(*.f64 x x)
▶	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
	21.4b	(+.f64 (.f64 x x) (.f64 y y))
▶	17.7b	(+.f64 (.f64 2 x) (.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	24.1b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 105 to 66 computations (37.1% saved)

localize23.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite66.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

576×	`pow1_binary64`
540×	`add-log-exp_binary64`
539×	`log1p-expm1-u_binary64`
539×	`expm1-log1p-u_binary64`
531×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	111	7
2	1418	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

Outputs

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

simplify190.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

29 → 22

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize6.0ms (0.1%)

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

localize7.0ms (0.1%)

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

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite76.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`pow1_binary64`
547×	`add-log-exp_binary64`
546×	`log1p-expm1-u_binary64`
546×	`expm1-log1p-u_binary64`
538×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	111	7
2	1433	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

Outputs

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

simplify184.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

29 → 22

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize17.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite78.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`pow1_binary64`
696×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
680×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	150	8
2	1954	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 2 x (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (*.f64 2 x) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2) (cbrt.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) (hypot.f64 y (sqrt.f64 (*.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 2 x) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 2 x) 2) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (-.f64 (*.f64 2 x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 2 x) 2)) (-.f64 (*.f64 y y) (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 2 x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 2 x)) 2) (cbrt.f64 (*.f64 2 x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 (*.f64 2 x)) (*.f64 y y))))))

simplify201.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
611×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	15	168
2	25	168
3	36	168
4	65	168
5	167	168
6	587	168
7	1453	168
8	1637	168
9	1821	168
10	2029	168
11	2324	168
12	2717	168
13	3202	168
14	3768	168
15	4456	168
16	5297	168
17	5691	168
18	5979	168
19	6255	168
20	6329	168
21	6363	168
22	7304	168

Stop Event

1×	node limit

Counts

59 → 39

Calls

Call 1

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

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))

eval45.0ms (1%)

Compiler: Compiled 937 to 565 computations (39.7% saved)

prune16.0ms (0.4%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	1	1
Picked	0	1	1
Done	1	4	5
Total	82	8	90

Error

Counts

90 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.0b	(*.f64 y y)
✓	44.9b	(*.f64 x x)
✓	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
▶	21.4b	(+.f64 (.f64 x x) (.f64 y y))
▶	24.0b	(+.f64 (.f64 x x) (.f64 2 x))
▶	41.7b	(*.f64 2 x)
✓	17.7b	(+.f64 (.f64 2 x) (.f64 y y))
✓	24.1b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 60 to 39 computations (35% saved)

localize4.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 9 computations (47.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite62.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

683×	`pow1_binary64`
641×	`add-log-exp_binary64`
640×	`log1p-expm1-u_binary64`
640×	`expm1-log1p-u_binary64`
627×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	133	7
2	1793	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 2 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 x 2))) (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) (hypot.f64 x (sqrt.f64 (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (/.f64 1 (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))) (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (*.f64 x (-.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (-.f64 (*.f64 x 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))))))

simplify170.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

51 → 44

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 5 computations (70.6% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite53.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	7
2	1751	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

Outputs

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

simplify167.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1204×	`sqr-pow_binary64`
754×	`cube-prod_binary64`
743×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
346×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	16	168
2	29	168
3	47	168
4	99	168
5	295	168
6	1113	168
7	1389	168
8	1679	168
9	1930	168
10	2269	168
11	2762	168
12	3421	168
13	4211	168
14	5133	168
15	5654	168
16	6071	168
17	6462	168
18	6583	168
19	6627	168
20	7796	168

Stop Event

1×	node limit

Counts

57 → 38

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))

eval22.0ms (0.5%)

Compiler: Compiled 921 to 561 computations (39.1% saved)

prune15.0ms (0.3%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	82	8	90

Error

Counts

90 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.0b	(*.f64 y y)
✓	44.9b	(*.f64 x x)
✓	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
✓	21.4b	(+.f64 (.f64 x x) (.f64 y y))
✓	24.0b	(+.f64 (.f64 x x) (.f64 2 x))
✓	41.7b	(*.f64 2 x)
✓	17.7b	(+.f64 (.f64 2 x) (.f64 y y))
✓	24.1b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 60 to 39 computations (35% saved)

regimes35.0ms (0.8%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	(+.f64 (.f64 x 2) (.f64 x x))
7.0ms	x
7.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
7.0ms	y
4.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 98 to 48 computations (51% saved)

regimes18.0ms (0.4%)

Counts

8 → 1

Calls

Call 1

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

Outputs
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))

Calls

3 calls:

7.0ms	x
5.0ms	y
4.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 57 to 27 computations (52.6% saved)

regimes67.0ms (1.5%)

Counts

7 → 3

Calls

Call 1

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

Outputs
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 x x) (.f64 y y))

Calls

3 calls:

29.0ms	y
24.0ms	x
13.0ms	(*.f64 y y)

Results

Error	Segments	Branch
1.4b	3	`x`
1.8b	5	`y`
1.9b	4	`(*.f64 y y)`

Compiler

Compiled 48 to 23 computations (52.1% saved)

bsearch43.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	1.309380535345464	79.24602107444342
22.0ms	-16023655.39004206	-0.0007685363598273775

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes46.0ms (1%)

Counts

6 → 3

Calls

Call 1

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

Outputs
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 x x) (.f64 2 x))
(+.f64 (.f64 x x) (.f64 y y))

Calls

3 calls:

19.0ms	x
15.0ms	y
10.0ms	(*.f64 y y)

Results

Error	Segments	Branch
15.8b	4	`x`
2.9b	3	`y`
3.1b	2	`(*.f64 y y)`

Compiler

Compiled 41 to 20 computations (51.2% saved)

bsearch40.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	6.580643267745813e-43	6.09825377561374e-22
19.0ms	-2.050568675011294e-100	-4.099674159309729e-104

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes52.0ms (1.2%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

27.0ms	x
15.0ms	y
9.0ms	(*.f64 y y)

Results

Error	Segments	Branch
16.3b	5	`x`
7.6b	3	`y`
8.5b	2	`(*.f64 y y)`

Compiler

Compiled 34 to 19 computations (44.1% saved)

bsearch44.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
22.0ms	6.580643267745813e-43	6.09825377561374e-22
21.0ms	-2.9639238159190677e-58	-1.8669427809793544e-59

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes49.0ms (1.1%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	x
14.0ms	y
9.0ms	(*.f64 y y)

Results

Error	Segments	Branch
16.3b	5	`x`
7.6b	3	`y`
8.5b	2	`(*.f64 y y)`

Compiler

Compiled 27 to 16 computations (40.7% saved)

bsearch44.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	6.580643267745813e-43	6.09825377561374e-22
22.0ms	-2.9639238159190677e-58	-1.8669427809793544e-59

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes49.0ms (1.1%)

Counts

3 → 5

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	x
15.0ms	y
14.0ms	(*.f64 y y)

Results

Error	Segments	Branch
18.9b	5	`x`
18.4b	4	`y`
18.3b	5	`(*.f64 y y)`

Compiler

Compiled 22 to 13 computations (40.9% saved)

bsearch79.0ms (1.8%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
21.0ms	9.20407117788922e-140	1.348323691091058e-128
20.0ms	2.762706390561362e-245	3.827449670168152e-238
18.0ms	2.554087250060537e-270	1.783637586083496e-264
20.0ms	4.87003390152761e-308	1.3908393682511158e-300

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes36.0ms (0.8%)

Accuracy

Total -41.2b remaining (-201.8%)

Threshold costs -41.2b (-201.8%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

3 calls:

15.0ms	x
12.0ms	y
7.0ms	(*.f64 y y)

Results

Error	Segments	Branch
32.3b	5	`x`
20.4b	3	`y`
20.6b	2	`(*.f64 y y)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

bsearch43.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	6.580643267745813e-43	6.09825377561374e-22
21.0ms	-2.050568675011294e-100	-4.099674159309729e-104

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	254
1	61	254

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(if (<=.f64 x -68821075862604768/4294967296) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 1474231422767003/1125899906842624) (+.f64 (.f64 2 x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -8079651963892742/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (+.f64 (.f64 x x) (.f64 2 x)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (+.f64 (.f64 x x) (.f64 2 x)) (.f64 y y)))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (.f64 (+.f64 2 x) x) (*.f64 y y)))
(if (<=.f64 (.f64 y y) 1232132294190227/25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848) (.f64 2 x) (if (<=.f64 (.f64 y y) 6076753482508067/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656) (.f64 x x) (if (<=.f64 (.f64 y y) 6796432087510455/246006311446272417135694895366447328831463738361430131889861407236509911043906984606020737387080298687645418100644428599105378407753391907201399550988776412284181771799458695654166637769167516870901097035133833253825096549816225533764062867857067136321933279232) (.f64 2 x) (if (<=.f64 (.f64 y y) 4936256741066367/53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786279785734596024336384) (.f64 x x) (*.f64 y y)))))
(if (<=.f64 y -8079651963892742/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (.f64 2 x) (*.f64 y y)))
(*.f64 2 x)

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 x 2)))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x (+.f64 x 2)))
(if (<=.f64 x -68821075862604768/4294967296) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 1474231422767003/1125899906842624) (+.f64 (.f64 2 x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 x -2150658620706399/134217728) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 1474231422767003/1125899906842624) (+.f64 (.f64 y y) (.f64 x 2)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -8079651963892742/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (+.f64 (.f64 x x) (.f64 2 x)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -4039825981946371/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 y 516342090949099/784637716923335095479473677900958302012794430558004314112) (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (+.f64 (.f64 x x) (.f64 2 x)) (.f64 y y)))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 516342090949099/784637716923335095479473677900958302012794430558004314112) (+.f64 (.f64 x x) (.f64 x 2)) (.f64 y y)))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (.f64 (+.f64 2 x) x) (*.f64 y y)))
(if (<=.f64 y -8378880151013365/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 y y) (if (<=.f64 y 516342090949099/784637716923335095479473677900958302012794430558004314112) (.f64 x (+.f64 x 2)) (*.f64 y y)))
(if (<=.f64 (.f64 y y) 1232132294190227/25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848) (.f64 2 x) (if (<=.f64 (.f64 y y) 6076753482508067/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656) (.f64 x x) (if (<=.f64 (.f64 y y) 6796432087510455/246006311446272417135694895366447328831463738361430131889861407236509911043906984606020737387080298687645418100644428599105378407753391907201399550988776412284181771799458695654166637769167516870901097035133833253825096549816225533764062867857067136321933279232) (.f64 2 x) (if (<=.f64 (.f64 y y) 4936256741066367/53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786279785734596024336384) (.f64 x x) (*.f64 y y)))))
(if (<=.f64 (.f64 y y) 1232132294190227/25300281663413827294061918339864663381194581220517764794612669753428792445999418361495047962679640561898384733039601488923726092173224184608376674992592313740189678034570795170558363467761652042654970959809093133570250935428086587327262919456144944542601257064044846194041676826903812816523290938580750782913463467636686848) (.f64 x 2) (if (<=.f64 (.f64 y y) 6076753482508067/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656) (.f64 x x) (if (<=.f64 (.f64 y y) 6796432087510455/246006311446272417135694895366447328831463738361430131889861407236509911043906984606020737387080298687645418100644428599105378407753391907201399550988776412284181771799458695654166637769167516870901097035133833253825096549816225533764062867857067136321933279232) (.f64 x 2) (if (<=.f64 (.f64 y y) 4936256741066367/53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786279785734596024336384) (.f64 x x) (*.f64 y y)))))
(if (<=.f64 y -8079651963892742/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (.f64 y y) (if (<=.f64 y 4130736727592792/6277101735386680763835789423207666416102355444464034512896) (.f64 2 x) (*.f64 y y)))
(if (<=.f64 y -4039825981946371/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) (.f64 y y) (if (<=.f64 y 516342090949099/784637716923335095479473677900958302012794430558004314112) (.f64 x 2) (*.f64 y y)))
(*.f64 2 x)
(*.f64 x 2)

Compiler

Compiled 195 to 103 computations (47.2% saved)

soundness0.0ms (0%)

end76.0ms (1.7%)

Compiler: Compiled 179 to 75 computations (58.1% saved)

Details

analyze100.0ms (2.2%)

sample1.5s (33.1%)

preprocess20.0ms (0.5%)

simplify8.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize12.0ms (0.3%)

series2.0ms (0%)

rewrite71.0ms (1.6%)

simplify192.0ms (4.3%)

localize17.0ms (0.4%)

series9.0ms (0.2%)

rewrite116.0ms (2.6%)

simplify198.0ms (4.4%)

eval45.0ms (1%)

prune29.0ms (0.7%)

localize23.0ms (0.5%)

series3.0ms (0.1%)

rewrite66.0ms (1.5%)

simplify190.0ms (4.2%)

localize6.0ms (0.1%)

localize7.0ms (0.1%)

localize12.0ms (0.3%)

series2.0ms (0%)

rewrite76.0ms (1.7%)

simplify184.0ms (4.1%)

localize17.0ms (0.4%)

series4.0ms (0.1%)

rewrite78.0ms (1.7%)

simplify201.0ms (4.5%)

eval45.0ms (1%)

prune16.0ms (0.4%)

localize4.0ms (0.1%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite62.0ms (1.4%)

simplify170.0ms (3.8%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite53.0ms (1.2%)

simplify167.0ms (3.7%)

eval22.0ms (0.5%)

prune15.0ms (0.3%)

regimes35.0ms (0.8%)

regimes18.0ms (0.4%)

regimes67.0ms (1.5%)

bsearch43.0ms (1%)

regimes46.0ms (1%)

bsearch40.0ms (0.9%)

regimes52.0ms (1.2%)

bsearch44.0ms (1%)

regimes49.0ms (1.1%)

bsearch44.0ms (1%)

regimes49.0ms (1.1%)

bsearch79.0ms (1.8%)

regimes36.0ms (0.8%)

bsearch43.0ms (1%)

simplify13.0ms (0.3%)

soundness0.0ms (0%)

end76.0ms (1.7%)

Profiling