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)

sample1.1s (50.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

preprocess47.0ms (2.2%)

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)

simplify36.0ms (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
	3.6b	(.f64 (cos.f64 x) (exp.f64 (.f64 10 (*.f64 x x))))
▶	3.2b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))

Compiler

Compiled 59 to 40 computations (32.2% saved)

localize8.0ms (0.4%)

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 (0.5%)

Counts

3 → 36

Calls

9 calls:

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

rewrite37.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

687×	`log1p-expm1-u_binary64`
687×	`expm1-log1p-u_binary64`
141×	`log-pow_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	163	29
2	1915	29

Stop Event

1×	node limit

Counts

3 → 53

simplify30.0ms (1.4%)

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

prune56.0ms (2.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	61	16	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	61	18	79

Error

0.6b

Counts

79 → 18

Alt Table

Status	Error	Program
	3.6b	(.f64 (cos.f64 x) (exp.f64 (.f64 10 (*.f64 x 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)))
▶	1.3b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))
	3.4b	(.f64 (cos.f64 x) (.f64 (pow.f64 (exp.f64 x) (*.f64 x 10)) 1))
✓	3.2b	(.f64 (cos.f64 x) (pow.f64 (exp.f64 (.f64 x 10)) x))
	3.4b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 x 10)) (cos.f64 x))) 3)
	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) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 20)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) x)))
	3.4b	(.f64 (cos.f64 x) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (.f64 x 10))) (sqrt.f64 (pow.f64 (exp.f64 x) (.f64 x 10)))))
	2.4b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (exp.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))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	3.4b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 x 10)) (cos.f64 x)) 3))
	3.7b	(.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) (.f64 x 10)))))
	2.1b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x)))

Compiler

Compiled 1438 to 923 computations (35.8% 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)

series14.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

4.0ms	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))	x	0
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	(pow.f64 (pow.f64 (exp.f64 10) x) x)	x	0
1.0ms	(pow.f64 (exp.f64 10) x)	x	0

rewrite39.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log1p-expm1-u_binary64`
694×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	166	29
2	1962	29

Stop Event

1×	node limit

Counts

3 → 53

simplify31.0ms (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

prune56.0ms (2.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	10	6	16
Picked	0	1	1
Done	1	0	1
Total	81	14	95

Error

0.2b

Counts

95 → 14

Alt Table

Status	Error	Program
	3.6b	(.f64 (cos.f64 x) (exp.f64 (.f64 10 (*.f64 x x))))
✓	1.3b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 10) x) x))
	3.1b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 10) (.f64 x x)) (cos.f64 x)) 3))
	2.4b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 x 10))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) 20) x))))
	0.5b	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))
	3.7b	(.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) (.f64 x 10)))))
	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)))
▶	0.4b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) 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)))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	2.0b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (exp.f64 10) (*.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))))
	3.4b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 x 10)) (cos.f64 x)) 3))
	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))

Compiler

Compiled 1385 to 912 computations (34.2% saved)

localize10.0ms (0.5%)

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)

series21.0ms (1%)

Counts

4 → 48

Calls

12 calls:

4.0ms	(*.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
3.0ms	(*.f64 (cos.f64 x) (sqrt.f64 (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
2.0ms	(pow.f64 (pow.f64 (exp.f64 20) x) x)	x	0

rewrite50.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
154×	`log1p-udef_binary64`
89×	`egg-rr`
88×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	185	42
2	2162	42

Stop Event

1×	node limit

Counts

4 → 89

simplify50.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-+l+_binary64`
447×	`distribute-lft-out_binary64`
347×	`*-commutative_binary64`
280×	`associate-+r+_binary64`
238×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	535
1	153	521
2	369	512
3	1159	511
4	2278	479
5	4854	479

Stop Event

1×	node limit

Counts

137 → 121

prune75.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	6	6	12
Picked	0	1	1
Done	1	0	1
Total	124	11	135

Error

0.2b

Counts

135 → 11

Alt Table

Status	Error	Program
	2.0b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (exp.f64 10) (*.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))))
▶	0.4b	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) x) (.f64 x 1/2)))
	0.6b	(.f64 (cos.f64 x) (.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (.f64 x 1/2)) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (.f64 x 1/2))))
	3.4b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 x 10)) (cos.f64 x)) 3))
	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))
	0.5b	(*.f64 (cos.f64 x) (sqrt.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 40) x) x))))
	0.9b	(.f64 (cos.f64 x) (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 40) x)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 20) x)) x))))
	3.1b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 10) (.f64 x x)) (cos.f64 x)) 3))
✓	0.4b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	0.5b	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))

Compiler

Compiled 2049 to 1358 computations (33.7% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 20) x)
✓	0.2b	(pow.f64 (pow.f64 (exp.f64 20) x) (*.f64 x 1/2))
✓	0.4b	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) x) (.f64 x 1/2)))

series12.0ms (0.6%)

Counts

2 → 24

Calls

6 calls:

3.0ms	(pow.f64 (pow.f64 (exp.f64 20) x) (*.f64 x 1/2))	x	inf
2.0ms	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) x) (.f64 x 1/2)))	x	-inf
2.0ms	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) x) (.f64 x 1/2)))	x	inf
2.0ms	(.f64 (cos.f64 x) (pow.f64 (pow.f64 (exp.f64 20) x) (.f64 x 1/2)))	x	0
2.0ms	(pow.f64 (pow.f64 (exp.f64 20) x) (*.f64 x 1/2))	x	0

rewrite41.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

880×	`log1p-expm1-u_binary64`
880×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-log-exp_binary64`
95×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	211	27
2	2503	27

Stop Event

1×	node limit

Counts

2 → 37

simplify27.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

447×	`fma-def_binary64`
373×	`associate-l_binary64`
325×	`unswap-sqr_binary64`
323×	`distribute-rgt-out_binary64`
319×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	400
1	97	328
2	227	276
3	678	276
4	2618	276

Stop Event

1×	node limit

Counts

61 → 54

prune47.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	78	11	89

Error

0.2b

Counts

89 → 11

Alt Table

Status	Error	Program
	0.6b	(.f64 (cos.f64 x) (.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (.f64 x 1/2)) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (.f64 x 1/2))))
	3.4b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 x 10)) (cos.f64 x)) 3))
	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))
	0.5b	(*.f64 (cos.f64 x) (sqrt.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 40) x) x))))
	0.9b	(.f64 (cos.f64 x) (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 40) x)) x) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 20) x)) x))))
	3.1b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 10) (.f64 x x)) (cos.f64 x)) 3))
✓	0.4b	(*.f64 (cos.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x)))
	0.6b	(.f64 (cos.f64 x) (pow.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) (sqrt.f64 (pow.f64 (exp.f64 20) x))) (*.f64 x 1/2)))
	2.2b	(*.f64 (cos.f64 x) (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 10)) 3) x))
	2.0b	(.f64 (cos.f64 x) (.f64 (cbrt.f64 (pow.f64 (exp.f64 10) (*.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 20) x) x))))
	0.5b	(*.f64 (cos.f64 x) (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 20) x)) x))

Compiler

Compiled 1277 to 866 computations (32.2% saved)

regimes135.0ms (6.4%)

Accuracy

Total 0.2b remaining (58.3%)

Threshold costs 0.2b (58.3%)

Counts

64 → 1

Compiler

Compiled 1882 to 1394 computations (25.9% saved)

simplify2.0ms (0.1%)

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

end192.0ms (9%)

Stop Event

1×

fuel

Compiler

Compiled 195 to 148 computations (24.1% saved)

Details

analyze1.0ms (0%)

sample1.1s (50.7%)

preprocess47.0ms (2.2%)

simplify36.0ms (1.7%)

prune4.0ms (0.2%)

localize8.0ms (0.4%)

series10.0ms (0.5%)

rewrite37.0ms (1.7%)

simplify30.0ms (1.4%)

prune56.0ms (2.6%)

localize9.0ms (0.4%)

series14.0ms (0.6%)

rewrite39.0ms (1.8%)

simplify31.0ms (1.4%)

prune56.0ms (2.6%)

localize10.0ms (0.5%)

series21.0ms (1%)

rewrite50.0ms (2.3%)

simplify50.0ms (2.4%)

prune75.0ms (3.5%)

localize10.0ms (0.5%)

series12.0ms (0.6%)

rewrite41.0ms (1.9%)

simplify27.0ms (1.3%)

prune47.0ms (2.2%)

regimes135.0ms (6.4%)

simplify2.0ms (0.1%)

end192.0ms (9%)

Profiling