Details

analyze8.0ms (0.3%)

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 6 computations (25% saved)

sample1.3s (45.2%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9
3	11	9

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

32.8b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(.f64 2 (.f64 x x))
6.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite120.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

884×	`log1p-udef_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
449×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`

Counts

2 → 71

Calls

2 calls:

116.0ms	(.f64 2 (.f64 x x))
116.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	121	13
2	1257	13
3	4991	13
4	6461	13
0	0	0
1	0	0

simplify141.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`fma-neg_binary64`
569×	`neg-mul-1_binary64`
441×	`fabs-mul_binary64`
416×	`distribute-rgt-neg-out_binary64`

Counts

95 → 75

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	41	164
3	76	164
4	160	164
5	416	164
6	614	164
7	992	164
8	1262	164
9	1713	164
10	2084	164
11	2649	164
12	2932	164
13	4196	164
14	4917	164
15	4747	164

prune85.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Error

0.1b

Counts

76 → 8

Alt Table

Status	Error	Program
▶	29.4b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	41.8b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	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) (sqrt.f64 (.f64 2 x)))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 912 to 694 computations (23.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite104.0ms (3.6%)

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:

103.0ms

(*.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

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune37.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	37	8	45

Error

0.1b

Counts

45 → 8

Alt Table

Status	Error	Program
✓	29.4b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	41.8b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	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) (sqrt.f64 (.f64 2 x)))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 459 to 379 computations (17.4% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.4%)

Counts

1 → 8

Calls

1 calls:

11.0ms

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

rewrite72.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

576×	`unpow-prod-down_binary64`
551×	`log1p-expm1-u_binary64`
551×	`expm1-log1p-u_binary64`
325×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

1 → 17

Calls

1 calls:

71.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	6
2	1486	6
3	5602	6
0	0	0
1	0	0

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

25 → 18

Iterations

Useful iterations: 0 (0.0ms)

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

prune24.0ms (0.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	18	8	26

Error

0.1b

Counts

26 → 8

Alt Table

Status	Error	Program
✓	29.4b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	41.8b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
▶	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) (sqrt.f64 (.f64 2 x)))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 259 to 208 computations (19.7% saved)

localize15.0ms (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))

series34.0ms (1.2%)

Counts

3 → 32

Calls

3 calls:

14.0ms	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
13.0ms	(.f64 (.f64 x (sqrt.f64 2)) (sqrt.f64 2))
7.0ms	(*.f64 x (sqrt.f64 2))

rewrite98.0ms (3.4%)

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:

97.0ms	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
97.0ms	(*.f64 x (sqrt.f64 2))
97.0ms	(.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

simplify183.0ms (6.4%)

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

prune43.0ms (1.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	36	9	45

Error

0.1b

Counts

45 → 9

Alt Table

Status	Error	Program
✓	29.4b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (.f64 2 (.f64 x 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))
	30.2b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 3) 1/2) (sqrt.f64 x))
	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	30.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	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) (sqrt.f64 (.f64 2 x)))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 583 to 450 computations (22.8% saved)

regimes300.0ms (10.4%)

Accuracy

Total 0.2b remaining (63.4%)

Threshold costs 0.2b (63.4%)

Counts

17 → 2

Compiler

Compiled 800 to 642 computations (19.8% saved)

bsearch24.0ms (0.8%)

Steps

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

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	20	25
2	28	25
3	33	25
4	38	25
5	40	25
6	40	25

end192.0ms (6.7%)

Compiler: Compiled 119 to 96 computations (19.3% saved)

Details

analyze8.0ms (0.3%)

sample1.3s (45.2%)

simplify13.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series13.0ms (0.5%)

rewrite120.0ms (4.2%)

simplify141.0ms (4.9%)

prune85.0ms (3%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite104.0ms (3.6%)

simplify10.0ms (0.4%)

prune37.0ms (1.3%)

localize8.0ms (0.3%)

series11.0ms (0.4%)

rewrite72.0ms (2.5%)

simplify13.0ms (0.5%)

prune24.0ms (0.8%)

localize15.0ms (0.5%)

series34.0ms (1.2%)

rewrite98.0ms (3.4%)

simplify183.0ms (6.4%)

prune43.0ms (1.5%)

regimes300.0ms (10.4%)

bsearch24.0ms (0.8%)

simplify6.0ms (0.2%)

end192.0ms (6.7%)

Profiling