Details

analyze372.0ms (8.1%)

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)

sample247.0ms (5.4%)

Algorithm

1×

intervals

Results

32.0ms	144×	body	2048	nan
16.0ms	256×	body	128	valid
13.0ms	78×	body	1024	nan
5.0ms	38×	body	512	nan
2.0ms	22×	body	256	nan
1.0ms	12×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify153.0ms (3.4%)

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

30.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	28.4b	(sqrt.f64 (fma.f64 x x -1))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

745×	`associate-/l*_binary64`
512×	`associate-/r*_binary64`
349×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
200×	`fma-def_binary64`

Counts

56 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	748
1	264	708
2	631	705
3	1895	695
4	4864	695
5	4886	695
6	4979	695

prune41.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Error

Counts

78 → 2

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1171 to 859 computations (26.6% saved)

localize5.0ms (0.1%)

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)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log-prod_binary64`
2×	`add-exp-log_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

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

simplify92.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

26 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	493
1	184	449
2	525	449
3	1696	449
4	4117	449
5	4962	449
6	4996	449
7	4927	449

prune21.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	38	2	40

Error

Counts

40 → 2

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 602 to 462 computations (23.3% saved)

regimes23.0ms (0.5%)

Accuracy

Total 0.2b remaining (79.6%)

Threshold costs 0.2b (79.6%)

Counts

6 → 1

Compiler

Compiled 174 to 124 computations (28.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample3.5s (76.8%)

Algorithm

1×

intervals

Results

1.3s	3929×	body	2048	nan
755.0ms	1933×	body	1024	nan
596.0ms	8000×	body	128	valid
157.0ms	982×	body	512	nan
39.0ms	460×	body	256	nan
21.0ms	447×	body	128	nan
2.0ms	6×	body	4096	nan

Compiler

Compiled 37 to 27 computations (27% saved)

Details

analyze372.0ms (8.1%)

sample247.0ms (5.4%)

simplify153.0ms (3.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify79.0ms (1.7%)

prune41.0ms (0.9%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify92.0ms (2%)

prune21.0ms (0.5%)

regimes23.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (76.8%)

Profiling