Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.2s (48.3%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

preprocess46.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

535×	`associate-/l/_binary64`
328×	`unswap-sqr_binary64`
297×	`associate-/r/_binary64`
247×	`associate-/l*_binary64`
218×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	14	14
2	25	14
3	48	14
4	108	14
5	281	14
6	822	14
7	1479	14
8	3786	14
9	4103	14
10	4643	14
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 7 computations (30% saved)

simplify42.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

535×	`associate-/l/_binary64`
328×	`unswap-sqr_binary64`
297×	`associate-/r/_binary64`
247×	`associate-/l*_binary64`
218×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	14	14
2	25	14
3	48	14
4	108	14
5	281	14
6	822	14
7	1479	14
8	3786	14
9	4103	14
10	4643	14

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

2.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.2b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))
	3.6b	(.f64 (cos.f64 x) (exp.f64 (.f64 10 (*.f64 x x))))

Compiler

Compiled 59 to 40 computations (32.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))
✓	0.4b	(pow.f64 (exp.f64 (*.f64 x 10)) x)
✓	2.6b	(exp.f64 (*.f64 x 10))

series10.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(pow.f64 (exp.f64 (*.f64 x 10)) x)	x	-inf
2.0ms	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))	x	-inf
2.0ms	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))	x	inf
1.0ms	(pow.f64 (exp.f64 (*.f64 x 10)) x)	x	0
1.0ms	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))	x	0

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
687×	`log1p-expm1-u_binary64`
687×	`expm1-log1p-u_binary64`
80×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	161	29
2	1886	29

Stop Event

1×	node limit

Counts

3 → 53

simplify32.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-def_binary64`
578×	`associate-l_binary64`
515×	`distribute-rgt-out_binary64`
471×	`unswap-sqr_binary64`
372×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	379
1	115	369
2	281	362
3	866	355
4	3512	355

Stop Event

1×	node limit

Counts

89 → 77

prune90.0ms (3.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	13	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	15	79

Error

0.7b

Counts

79 → 15

Alt Table

Status	Error	Program
✓	3.2b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	3.6b	(.f64 (cos.f64 x) (exp.f64 (.f64 10 (*.f64 x x))))
	3.7b	(pow.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x (*.f64 x 10))) (cos.f64 x))) 3)
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 20)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) x)))
▶	1.3b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))
	2.1b	(.f64 (cos.f64 x) (pow.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) (cbrt.f64 (pow.f64 (exp.f64 x) 20))) x))
	2.1b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x)))
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (pow.f64 (exp.f64 x) 5) x) (pow.f64 (pow.f64 (exp.f64 x) 5) x)))
	3.7b	(.f64 (cos.f64 x) (.f64 (sqrt.f64 (exp.f64 (.f64 x (.f64 x 10)))) (sqrt.f64 (exp.f64 (.f64 x (.f64 x 10))))))
	2.5b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (exp.f64 (.f64 x (.f64 x 10)))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x))))
	3.4b	(*.f64 (cos.f64 x) (pow.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) 10))) x))
	2.1b	(*.f64 (cos.f64 x) (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 10) 3)) x))
	3.6b	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 1) (.f64 x 10)) x))
	2.1b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (pow.f64 (exp.f64 x) 5) 2) x))

Compiler

Compiled 1366 to 900 computations (34.1% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))
✓	0.4b	(pow.f64 (pow.f64 (exp.f64 10) x) x)
✓	1.0b	(pow.f64 (exp.f64 10) x)

series15.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

4.0ms	(pow.f64 (exp.f64 10) x)	x	-inf
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))	x	-inf
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))	x	inf
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))	x	0
2.0ms	(pow.f64 (pow.f64 (exp.f64 10) x) x)	x	0

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

750×	`pow1_binary64`
694×	`log1p-expm1-u_binary64`
694×	`expm1-log1p-u_binary64`
81×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	164	29
2	1919	29

Stop Event

1×	node limit

Counts

3 → 53

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
573×	`associate-l_binary64`
487×	`unswap-sqr_binary64`
385×	`associate-r_binary64`
139×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	379
1	125	369
2	296	362
3	924	355
4	3924	355

Stop Event

1×	node limit

Counts

89 → 77

prune54.0ms (2.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	6	7	13
Picked	0	1	1
Done	0	1	1
Total	76	16	92

Error

0.3b

Counts

92 → 16

Alt Table

Status	Error	Program
✓	3.2b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	3.1b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 10) (.f64 x x)) (cos.f64 x)) 3))
	3.1b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 10) (.f64 x x)))
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 20)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) x)))
✓	1.3b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))
	3.2b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (exp.f64 20)) (.f64 x x)) (pow.f64 (cbrt.f64 (exp.f64 10)) (.f64 x x))))
	3.7b	(pow.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x (*.f64 x 10))) (cos.f64 x))) 3)
▶	0.5b	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))
	1.1b	(.f64 (cos.f64 x) (pow.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 10)) x) (pow.f64 (sqrt.f64 (exp.f64 10)) x)) x))
	2.1b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x)))
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (pow.f64 (exp.f64 x) 5) x) (pow.f64 (pow.f64 (exp.f64 x) 5) x)))
	3.7b	(.f64 (cos.f64 x) (.f64 (sqrt.f64 (exp.f64 (.f64 x (.f64 x 10)))) (sqrt.f64 (exp.f64 (.f64 x (.f64 x 10))))))
	2.5b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (exp.f64 (.f64 x (.f64 x 10)))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x))))
	1.2b	(.f64 (cos.f64 x) (.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 10) x)) x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 10) x)) x)))
	1.4b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 20) x)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 10) x)) x)))

Compiler

Compiled 1445 to 949 computations (34.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 20) x)
✓	0.1b	(sqrt.f64 (pow.f64 (exp.f64 20) x))
✓	0.4b	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))
✓	0.4b	(pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x)

series21.0ms (0.8%)

Counts

4 → 40

Calls

12 calls:

6.0ms	(sqrt.f64 (pow.f64 (exp.f64 20) x))	x	0
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))	x	-inf
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))	x	inf
2.0ms	(pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x)	x	0
2.0ms	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))	x	0

rewrite59.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`pow1_binary64`
760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	41
1	183	41
2	2117	41

Stop Event

1×	node limit

Counts

4 → 85

simplify38.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

657×	`associate-l_binary64`
562×	`distribute-rgt-out_binary64`
503×	`unswap-sqr_binary64`
441×	`associate-r_binary64`
248×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	430
1	149	418
2	367	408
3	1140	406
4	3288	374

Stop Event

1×	node limit

Counts

125 → 115

prune97.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	12	1	13
Picked	1	0	1
Done	2	0	2
Total	121	10	131

Error

0.1b

Counts

131 → 10

Alt Table

Status	Error	Program
	1.1b	(.f64 (cos.f64 x) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (exp.f64 40) x))) (sqrt.f64 (cbrt.f64 (pow.f64 (exp.f64 20) x)))) x))
	0.8b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))))
	0.7b	(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) 3) (pow.f64 (cos.f64 x) 3)))
	0.7b	(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) (cos.f64 x)) 3))
	1.2b	(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) (cos.f64 x))) 3)
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 20)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) x)))
	0.7b	(*.f64 (cos.f64 x) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) 3)))
▶	0.4b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))
	1.0b	(.f64 (cos.f64 x) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 20) x) 1/4) x) (pow.f64 (pow.f64 (pow.f64 (exp.f64 20) x) 1/4) x)))
	0.5b	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) (.f64 x 1/2)) x))

Compiler

Compiled 1945 to 1364 computations (29.9% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 20) x)
✓	0.1b	(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))
✓	0.4b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))
✓	0.5b	(pow.f64 (pow.f64 (exp.f64 20) x) x)

series20.0ms (0.8%)

Counts

3 → 36

Calls

9 calls:

5.0ms	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))	x	-inf
3.0ms	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))	x	inf
2.0ms	(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))	x	-inf
2.0ms	(pow.f64 (pow.f64 (exp.f64 20) x) x)	x	0
2.0ms	(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))	x	inf

rewrite49.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`pow1_binary64`
764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	183	36
2	2121	36

Stop Event

1×	node limit

Counts

3 → 72

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
437×	`associate-l_binary64`
432×	`distribute-lft-out_binary64`
411×	`distribute-rgt-out_binary64`
342×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	444
1	120	432
2	285	426
3	813	426
4	3021	394

Stop Event

1×	node limit

Counts

108 → 97

prune99.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.1b

Counts

135 → 10

Alt Table

Status	Error	Program
	1.1b	(.f64 (cos.f64 x) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (exp.f64 40) x))) (sqrt.f64 (cbrt.f64 (pow.f64 (exp.f64 20) x)))) x))
	0.8b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))))
	0.7b	(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) 3) (pow.f64 (cos.f64 x) 3)))
	0.7b	(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) (cos.f64 x)) 3))
	1.2b	(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) (cos.f64 x))) 3)
	0.6b	(.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (pow.f64 (pow.f64 (exp.f64 20) x) 1/4)) (pow.f64 (pow.f64 (exp.f64 20) x) 1/4)) x)))
	2.1b	(.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 20)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) x)))
	0.7b	(*.f64 (cos.f64 x) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x) 3)))
	1.0b	(.f64 (cos.f64 x) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 20) x) 1/4) x) (pow.f64 (pow.f64 (pow.f64 (exp.f64 20) x) 1/4) x)))
	0.5b	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) (.f64 x 1/2)) x))

Compiler

Compiled 2005 to 1319 computations (34.2% saved)

regimes234.0ms (9.4%)

Accuracy

Total 0.3b remaining (69.1%)

Threshold costs 0.3b (69.1%)

Counts

113 → 1

Compiler

Compiled 3256 to 2464 computations (24.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	18	17

Stop Event

1×

saturated

end181.0ms (7.3%)

Stop Event

1×

fuel

Compiler

Compiled 199 to 153 computations (23.1% saved)

Details

analyze1.0ms (0%)

sample1.2s (48.3%)

preprocess46.0ms (1.9%)

simplify42.0ms (1.7%)

prune4.0ms (0.2%)

localize8.0ms (0.3%)

series10.0ms (0.4%)

rewrite42.0ms (1.7%)

simplify32.0ms (1.3%)

prune90.0ms (3.6%)

localize9.0ms (0.4%)

series15.0ms (0.6%)

rewrite42.0ms (1.7%)

simplify34.0ms (1.4%)

prune54.0ms (2.2%)

localize10.0ms (0.4%)

series21.0ms (0.8%)

rewrite59.0ms (2.4%)

simplify38.0ms (1.5%)

prune97.0ms (3.9%)

localize11.0ms (0.4%)

series20.0ms (0.8%)

rewrite49.0ms (2%)

simplify34.0ms (1.4%)

prune99.0ms (4%)

regimes234.0ms (9.4%)

simplify4.0ms (0.2%)

end181.0ms (7.3%)

Profiling