Details

analyze366.0ms (6.1%)

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)

sample237.0ms (4%)

Algorithm

1×

intervals

Results

26.0ms	123×	body	2048	nan
18.0ms	256×	body	128	valid
10.0ms	60×	body	1024	nan
3.0ms	28×	body	512	nan
1.0ms	14×	body	256	nan
1.0ms	15×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify156.0ms (2.6%)

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%)

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

35.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	0.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	33.1b	(sqrt.f64 (fma.f64 x x -1))

series13.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms	(sqrt.f64 (fma.f64 x x -1))
3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 49

Calls

3 calls:

5.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
330×	`sub-neg_binary64`
301×	`fma-def_binary64`
254×	`distribute-neg-frac_binary64`
210×	`associate-+l+_binary64`

Counts

85 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1395
1	401	1305
2	1052	1265
3	3424	1265
4	4773	1265
5	4915	1265

prune83.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Error

Counts

119 → 3

Alt Table

Status	Error	Program
	35.6b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
	0.7b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
▶	0.4b	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))

Compiler

Compiled 1951 to 1459 computations (25.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 5/96 (pow.f64 x 6))
✓	0.2b	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))
✓	0.3b	(/.f64 3/32 (pow.f64 x 4))
✓	0.5b	(/.f64 1/4 (*.f64 x x))

series14.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

5.0ms	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))
3.0ms	(/.f64 5/96 (pow.f64 x 6))
3.0ms	(/.f64 3/32 (pow.f64 x 4))
3.0ms	(/.f64 1/4 (*.f64 x x))

rewrite275.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

724×	`add-sqr-sqrt_binary64`
655×	`*-un-lft-identity_binary64`
559×	`times-frac_binary64`
516×	`associate-+r+_binary64`
453×	`prod-diff_binary64`

Counts

4 → 667

Calls

4 calls:

76.0ms	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))
4.0ms	(/.f64 3/32 (pow.f64 x 4))
3.0ms	(/.f64 1/4 (*.f64 x x))
3.0ms	(/.f64 5/96 (pow.f64 x 6))

simplify612.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary64`
322×	`associate-*r/_binary64`
302×	`+-commutative_binary64`
297×	`log-div_binary64`
273×	`fma-udef_binary64`

Counts

691 → 814

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	960	25157
1	2077	22442
2	3522	21713
3	4162	21713
4	4849	21713

prune1.2s (20.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	814	0	814
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	814	3	817

Error

Counts

817 → 3

Alt Table

Status	Error	Program
	35.6b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
▶	0.7b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	0.4b	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))

Compiler

Compiled 46181 to 34525 computations (25.2% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(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)))

simplify94.0ms (1.6%)

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

prune28.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
▶	35.6b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓	0.7b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	0.4b	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))

Compiler

Compiled 639 to 491 computations (23.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.3b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓	6.0b	(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))
	33.1b	(sqrt.f64 (fma.f64 x x -1))

series19.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
5.0ms	(log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms	(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`
4×	`pow1_binary64`

Counts

3 → 36

Calls

3 calls:

1.0ms	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
0.0ms	(log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-neg_binary64`
379×	`fma-def_binary64`
320×	`times-frac_binary64`
277×	`associate-+l+_binary64`
245×	`associate-/r*_binary64`

Counts

72 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	1412
1	441	1277
2	1337	1259
3	4785	1259
4	5375	1259

prune91.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	35.6b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓	0.7b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	0.4b	(+.f64 (log.f64 2) (-.f64 (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))) (/.f64 5/96 (pow.f64 x 6))))

Compiler

Compiled 2689 to 2103 computations (21.8% saved)

regimes118.0ms (2%)

Accuracy

Total 0.3b remaining (99%)

Threshold costs 0.3b (99%)

Counts

41 → 1

Compiler

Compiled 1782 to 1321 computations (25.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`*-commutative_binary64`
11×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	47
1	35	47
2	43	47
3	62	47
4	81	47
5	109	47
6	122	47
7	128	47
8	130	47
9	125	47

end1.0ms (0%)

Compiler: Compiled 32 to 28 computations (12.5% saved)

sample2.4s (40.9%)

Algorithm

1×

intervals

Results

907.0ms	4090×	body	2048	nan
477.0ms	8000×	body	128	valid
358.0ms	2025×	body	1024	nan
141.0ms	1066×	body	512	nan
43.0ms	516×	body	256	nan
26.0ms	498×	body	128	nan
2.0ms	7×	body	4096	nan

Compiler

Compiled 87 to 70 computations (19.5% saved)

Details

analyze366.0ms (6.1%)

sample237.0ms (4%)

simplify156.0ms (2.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series13.0ms (0.2%)

rewrite10.0ms (0.2%)

simplify79.0ms (1.3%)

prune83.0ms (1.4%)

localize16.0ms (0.3%)

series14.0ms (0.2%)

rewrite275.0ms (4.6%)

simplify612.0ms (10.2%)

prune1.2s (20.2%)

localize9.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify94.0ms (1.6%)

prune28.0ms (0.5%)

localize10.0ms (0.2%)

series19.0ms (0.3%)

rewrite3.0ms (0%)

simplify70.0ms (1.2%)

prune91.0ms (1.5%)

regimes118.0ms (2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.4s (40.9%)

Profiling