Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.3s (35.6%)

Results

952.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify230.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune6.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(fma.f64 6 x -6)
✓	0.3b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series53.0ms (1.4%)

Counts

3 → 18

Calls

3 calls:

43.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
6.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
3.0ms	(fma.f64 6 x -6)

rewrite69.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

439×	`log-prod_binary64`
188×	`log1p-udef_binary64`
187×	`expm1-udef_binary64`
174×	`prod-diff_binary64`
171×	`pow3_binary64`

Counts

3 → 94

Calls

3 calls:

66.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
66.0ms	(fma.f64 6 x -6)
66.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	233	32
2	2592	32
3	4862	32
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-neg_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

112 → 101

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	60
1	13	60
2	15	60
3	13	60

prune116.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Error

0.0b

Counts

103 → 8

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
	0.4b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	33.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.3b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
	13.6b	(/.f64 (fma.f64 6 x -6) (/.f64 (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1))))
	33.5b	6
	33.0b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 2045 to 1509 computations (26.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
	0.0b	(fma.f64 6 x -6)
✓	0.3b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

series21.0ms (0.6%)

Counts

2 → 5

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)

rewrite94.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

447×	`log-prod_binary64`
259×	`prod-diff_binary64`
188×	`log1p-udef_binary64`
187×	`expm1-udef_binary64`
167×	`fma-def_binary64`

Counts

2 → 71

Calls

2 calls:

93.0ms	(fma.f64 4 (sqrt.f64 x) x)
92.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	233	24
2	2615	24
3	4916	24
4	4973	24
0	0	0
1	0	0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

76 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	3	5

prune84.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Status	Error	Program
	13.7b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.3b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
▶	1.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
	33.5b	6
	33.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 1972 to 1436 computations (27.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 6 x -6)
✓	0.1b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
	0.3b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.0b	(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series111.0ms (3%)

Counts

2 → 6

Calls

2 calls:

74.0ms	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
36.0ms	(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite72.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

506×	`log-prod_binary64`
214×	`log1p-udef_binary64`
213×	`expm1-udef_binary64`
182×	`log-pow_binary64`
174×	`prod-diff_binary64`

Counts

2 → 83

Calls

2 calls:

70.0ms	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
70.0ms	(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	280	36
2	2991	36
3	5280	36
0	0	0
1	0	0

simplify123.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1412×	`sqr-pow_binary64`
616×	`associate-l_binary64`
616×	`cube-prod_binary64`
512×	`pow-sqr_binary64`
504×	`fabs-mul_binary64`

Counts

89 → 91

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	25	18
2	36	18
3	63	18
4	135	18
5	335	18
6	1021	18
7	1098	18
8	1354	18
9	1706	18
10	2188	18
11	2819	18
12	3101	18
13	3230	18
14	3369	18
15	3455	18
16	3588	18
17	4505	18
18	4988	18

prune250.0ms (6.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
▶	13.7b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.3b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	1.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
	33.5b	6
	33.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 3406 to 2592 computations (23.9% saved)

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 6 x -6)
✓	0.1b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.2b	(pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2)
✓	13.2b	(/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1))

series104.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

48.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

37.0ms

(/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1))

19.0ms

(pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2)

rewrite126.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

301×	`prod-diff_binary64`
263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`

Counts

3 → 98

Calls

3 calls:

121.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

121.0ms

(pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2)

121.0ms

(/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	62
1	341	47
2	3751	47
3	4993	47
0	0	0
1	0	0

simplify116.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-/l/_binary64`
516×	`fma-def_binary64`
460×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
354×	`distribute-rgt-in_binary64`

Counts

107 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	20	27
2	33	25
3	72	25
4	163	25
5	390	25
6	1055	25
7	1831	25
8	3375	25
9	4665	25
10	4927	25
11	4988	25
12	4832	25

prune250.0ms (6.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	13.7b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) -1)) (-.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.3b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	1.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
	33.5b	6
	33.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 3686 to 2614 computations (29.1% saved)

regimes262.0ms (7.1%)

Accuracy

Total 0.2b remaining (91.2%)

Threshold costs 0.2b (91.2%)

Counts

61 → 1

Compiler

Compiled 2243 to 1774 computations (20.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	14	17
2	13	17

end199.0ms (5.4%)

Compiler: Compiled 95 to 74 computations (22.1% saved)

Details

analyze3.0ms (0.1%)

sample1.3s (35.6%)

simplify230.0ms (6.3%)

prune6.0ms (0.2%)

localize9.0ms (0.2%)

series53.0ms (1.4%)

rewrite69.0ms (1.9%)

simplify10.0ms (0.3%)

prune116.0ms (3.2%)

localize12.0ms (0.3%)

series21.0ms (0.6%)

rewrite94.0ms (2.6%)

simplify7.0ms (0.2%)

prune84.0ms (2.3%)

localize10.0ms (0.3%)

series111.0ms (3%)

rewrite72.0ms (2%)

simplify123.0ms (3.4%)

prune250.0ms (6.8%)

localize26.0ms (0.7%)

series104.0ms (2.8%)

rewrite126.0ms (3.4%)

simplify116.0ms (3.2%)

prune250.0ms (6.8%)

regimes262.0ms (7.1%)

simplify4.0ms (0.1%)

end199.0ms (5.4%)

Profiling