Details

analyze34.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.2s (64.3%)

Results

1.1s	8256×	body	128	valid
49.0ms	392×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify53.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	13.0b	(/.f64 b (*.f64 a a))

series36.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(/.f64 b (*.f64 a a))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite45.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
142×	`log1p-udef_binary64`
90×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Counts

2 → 59

Calls

2 calls:

44.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
44.0ms	(/.f64 b (*.f64 a a))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	182	20
2	1989	20
3	4975	20

simplify110.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1214×	`fma-def_binary64`
706×	`associate-/r/_binary64`
598×	`div-sub_binary64`
525×	`fma-neg_binary64`
434×	`unswap-sqr_binary64`

Counts

107 → 62

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	528
1	17	528
2	29	528
3	54	528
4	120	528
5	336	528
6	1160	528
7	1957	528
8	2364	528
9	2778	528
10	3554	528
11	4092	528
12	4278	528
13	4997	528

prune29.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	1	63

Error

0.0b

Counts

63 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 874 to 461 computations (47.3% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
✓	0.2b	(/.f64 (sqrt.f64 b) a)
✓	0.5b	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)

series40.0ms (2.1%)

Counts

3 → 48

Calls

3 calls:

17.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
9.0ms	(/.f64 (sqrt.f64 b) a)

rewrite51.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
104×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`
98×	`add-log-exp_binary64`

Counts

3 → 97

Calls

3 calls:

49.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
49.0ms	(/.f64 (sqrt.f64 b) a)
49.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	221	26
2	2217	26
3	5184	26

simplify92.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

618×	`unswap-sqr_binary64`
568×	`fma-def_binary64`
412×	`associate-/l*_binary64`
361×	`fma-neg_binary64`
317×	`*-commutative_binary64`

Counts

145 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	672
1	29	564
2	57	516
3	170	516
4	700	516
5	1694	516
6	2108	516
7	2766	516
8	3807	516
9	4825	516
10	4942	516

prune66.0ms (3.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	1	101

Error

0.0b

Counts

101 → 1

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 1492 to 773 computations (48.2% saved)

regimes55.0ms (2.9%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

7 → 1

Compiler

Compiled 811 to 525 computations (35.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	11	17

end42.0ms (2.2%)

Compiler: Compiled 39 to 30 computations (23.1% saved)

Details

analyze34.0ms (1.8%)

sample1.2s (64.3%)

simplify53.0ms (2.8%)

prune3.0ms (0.2%)

localize8.0ms (0.4%)

series36.0ms (1.9%)

rewrite45.0ms (2.4%)

simplify110.0ms (5.8%)

prune29.0ms (1.5%)

localize7.0ms (0.4%)

series40.0ms (2.1%)

rewrite51.0ms (2.7%)

simplify92.0ms (4.9%)

prune66.0ms (3.5%)

regimes55.0ms (2.9%)

simplify2.0ms (0.1%)

end42.0ms (2.2%)

Profiling