Details

analyze10.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.1s (52%)

Results

905.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify140.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

32.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	31.6b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series6.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
2.0ms	(*.f64 2 (pow.f64 x 2))

rewrite83.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

850×	`log1p-udef_binary64`
450×	`log1p-expm1-u_binary64`
450×	`expm1-log1p-u_binary64`
402×	`unpow-prod-down_binary64`
251×	`log-prod_binary64`

Counts

2 → 72

Calls

2 calls:

81.0ms	(*.f64 2 (pow.f64 x 2))
81.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1214	13
3	4880	13
4	6252	13
0	0	0
1	0	0

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

84 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune50.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Error

0.1b

Counts

75 → 7

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	46.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
	30.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	29.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	29.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 856 to 669 computations (21.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 (sqrt.f64 2) x)

rewrite77.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

711×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
336×	`pow1_binary64`
245×	`unpow-prod-down_binary64`

Counts

1 → 37

Calls

1 calls:

76.0ms

(*.f64 (sqrt.f64 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	0	0
1	0	0

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune19.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	37	7	44

Error

0.1b

Counts

44 → 7

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	46.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
	30.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
▶	29.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	29.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 431 to 362 computations (16% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))

series6.0ms (0.3%)

Counts

1 → 8

Calls

1 calls:

6.0ms

(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x 2) 1/2))

rewrite42.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

613×	`log1p-expm1-u_binary64`
613×	`expm1-log1p-u_binary64`
348×	`log-prod_binary64`
127×	`expm1-udef_binary64`
127×	`log1p-udef_binary64`

Counts

1 → 19

Calls

1 calls:

41.0ms

(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x 2) 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	164	6
2	1644	6
3	4890	6
0	0	0
1	0	0

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

27 → 20

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	48
1	6	48
2	6	48

prune12.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	20	7	27

Error

0.1b

Counts

27 → 7

Alt Table

Status	Error	Program
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	46.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
▶	30.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	29.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	29.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 255 to 206 computations (19.2% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	0.4b	(.f64 (.f64 x (sqrt.f64 2)) (sqrt.f64 2))

series18.0ms (0.9%)

Counts

3 → 32

Calls

3 calls:

8.0ms	(.f64 (.f64 x (sqrt.f64 2)) (sqrt.f64 2))
7.0ms	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
3.0ms	(*.f64 x (sqrt.f64 2))

rewrite82.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

709×	`log1p-expm1-u_binary64`
709×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
134×	`log-pow_binary64`

Counts

3 → 52

Calls

3 calls:

81.0ms	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
81.0ms	(*.f64 x (sqrt.f64 2))
81.0ms	(.f64 (.f64 x (sqrt.f64 2)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	204	16
2	1892	16
3	4949	16
4	4931	16
0	0	0
1	0	0

simplify155.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1710×	`unswap-sqr_binary64`
1171×	`sqr-pow_binary64`
561×	`pow-sqr_binary64`
542×	`fabs-mul_binary64`
529×	`cube-prod_binary64`

Counts

84 → 37

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	228
1	14	168
2	22	168
3	36	168
4	70	168
5	182	168
6	551	168
7	737	168
8	784	168
9	903	168
10	1053	168
11	1263	168
12	1478	168
13	1706	168
14	2042	168
15	2486	168
16	3036	168
17	3327	168
18	3533	168
19	3599	168
20	3622	168
21	3636	168
22	4177	168
23	7512	168

prune22.0ms (1.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	35	9	44

Error

0.1b

Counts

44 → 9

Alt Table

Status	Error	Program
✓	29.4b	(*.f64 (sqrt.f64 2) x)
	30.2b	(.f64 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	46.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
✓	30.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	29.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.2b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 3) 1/2) (sqrt.f64 x))

Compiler

Compiled 582 to 451 computations (22.5% saved)

regimes97.0ms (4.7%)

Accuracy

Total 0.3b remaining (64.4%)

Threshold costs 0.3b (64.4%)

Counts

16 → 2

Compiler

Compiled 690 to 578 computations (16.2% saved)

bsearch18.0ms (0.8%)

Steps

Iters	Range		Point
9	-7.0290898584775714e-304	1.0895490308086033e-304	6.07190567874543e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	26
2	34	26
3	39	26
4	41	26
5	41	26

end105.0ms (5.1%)

Compiler: Compiled 120 to 99 computations (17.5% saved)

Details

analyze10.0ms (0.5%)

sample1.1s (52%)

simplify140.0ms (6.7%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite83.0ms (4%)

simplify12.0ms (0.6%)

prune50.0ms (2.4%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite77.0ms (3.7%)

simplify6.0ms (0.3%)

prune19.0ms (0.9%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite42.0ms (2%)

simplify7.0ms (0.3%)

prune12.0ms (0.6%)

localize10.0ms (0.5%)

series18.0ms (0.9%)

rewrite82.0ms (4%)

simplify155.0ms (7.4%)

prune22.0ms (1.1%)

regimes97.0ms (4.7%)

bsearch18.0ms (0.8%)

simplify3.0ms (0.1%)

end105.0ms (5.1%)

Profiling