Details

analyze379.0ms (13.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.9s (68.2%)

Results

906.0ms	8256×	body	128	valid
827.0ms	8224×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify157.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
804×	`unsub-neg_binary64`
461×	`distribute-neg-in_binary64`
434×	`sub-neg_binary64`
338×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	64	12
5	113	12
6	247	12
7	500	12
8	1560	12
9	2513	12
10	3218	12
11	3602	12
12	3803	12
13	3974	12
14	4075	12
15	4392	12
16	4836	12
17	4898	12
18	4901	12

prune3.0ms (0.1%)

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

32.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	30.1b	(sqrt.f64 (fma.f64 x x -1))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(sqrt.f64 (fma.f64 x x -1))
3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite42.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

615×	`prod-diff_binary64`
610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
108×	`log1p-udef_binary64`
61×	`add-sqr-sqrt_binary64`

Counts

2 → 58

Calls

2 calls:

41.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
41.0ms	(sqrt.f64 (fma.f64 x x -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	124	17
2	1517	17
3	5046	17
0	0	0
1	0	0

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

743×	`associate-/l*_binary64`
656×	`fma-def_binary64`
512×	`associate-/r*_binary64`
283×	`associate-*l/_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

82 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	396
1	187	377
2	475	375
3	1486	366
4	4834	366
5	4977	366
6	4917	366

prune49.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
▶	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	32.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 1495 to 1079 computations (27.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

rewrite38.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
283×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

1 → 26

Calls

1 calls:

38.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	145	10
2	1600	10
3	4870	10
0	0	0
1	0	0

simplify50.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
535×	`times-frac_binary64`
409×	`cancel-sign-sub-inv_binary64`
345×	`sub-neg_binary64`
309×	`fma-neg_binary64`

Counts

38 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	272
1	162	258
2	499	258
3	1660	258
4	4407	258
5	5124	258

prune24.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	48	2	50

Error

Counts

50 → 2

Alt Table

Status	Error	Program
✓	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	32.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 727 to 561 computations (22.8% saved)

regimes23.0ms (0.8%)

Accuracy

Total 0.2b remaining (93.1%)

Threshold costs 0.2b (93.1%)

Counts

6 → 1

Compiler

Compiled 174 to 124 computations (28.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end40.0ms (1.4%)

Compiler: Compiled 33 to 24 computations (27.3% saved)

Details

analyze379.0ms (13.5%)

sample1.9s (68.2%)

simplify157.0ms (5.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite42.0ms (1.5%)

simplify65.0ms (2.3%)

prune49.0ms (1.7%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite38.0ms (1.4%)

simplify50.0ms (1.8%)

prune24.0ms (0.8%)

regimes23.0ms (0.8%)

simplify2.0ms (0.1%)

end40.0ms (1.4%)

Profiling