Details

analyze1.0s (11.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample6.4s (70%)

Results

3.0s	4186×	body	1024	valid
1.2s	2042×	body	1024	invalid
871.0ms	2112×	body	512	valid
384.0ms	1018×	body	512	invalid
297.0ms	1068×	body	256	valid
253.0ms	234×	body	2048	valid
140.0ms	532×	body	256	invalid
123.0ms	814×	body	128	invalid
95.0ms	656×	body	128	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify130.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
444×	`times-frac_binary64`
419×	`sub-neg_binary64`
365×	`distribute-rgt-neg-in_binary64`
340×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	23	18
2	49	18
3	106	18
4	225	17
5	449	17
6	962	17
7	1713	17
8	3588	17
9	4282	17
10	4773	17
11	4923	17
12	4957	17
13	4748	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

45.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	6.3b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series17.0ms (0.2%)

Counts

2 → 32

Calls

2 calls:

14.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite61.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite
2×	egg-rewrite

Rules

116×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`
108×	`add-log-exp_binary64`
106×	`add-cbrt-cube_binary64`

Counts

2 → 0

Calls

2 calls:

61.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
61.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	228	20
2	27	20
0	6	10
1	127	10
2	70	10
0	11	18
1	228	18
2	27	18
0	0	0
1	0	0

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
412×	`sub-neg_binary64`
382×	`distribute-rgt-neg-in_binary64`
359×	`distribute-lft-neg-in_binary64`
297×	`neg-mul-1_binary64`

Counts

32 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	734
1	297	716
2	990	666
3	3580	666
4	4813	666
5	4949	666

prune26.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Error

0.1b

Counts

29 → 3

Alt Table

Status	Error	Program
▶	0.9b	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	47.6b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (.f64 (exp.f64 im) re) -1/2)))
✓	45.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 712 to 435 computations (38.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) -1/6))
✓	0.1b	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	0.1b	(*.f64 (pow.f64 im 3) -1/6)

series31.0ms (0.3%)

Counts

3 → 48

Calls

3 calls:

25.0ms	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
3.0ms	(+.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) -1/6))
3.0ms	(*.f64 (pow.f64 im 3) -1/6)

rewrite102.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
367×	`fma-def_binary64`
261×	`egg-rr`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`

Counts

3 → 261

Calls

3 calls:

97.0ms	(+.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) -1/6))
97.0ms	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
97.0ms	(*.f64 (pow.f64 im 3) -1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	242	28
2	2661	28
3	4983	28
4	4851	28
0	0	0
1	0	0

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-def_binary64`
390×	`associate-l_binary64`
357×	`distribute-lft-out_binary64`
337×	`sub-neg_binary64`
312×	`associate-r_binary64`

Counts

309 → 281

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	677
1	197	672
2	712	646
3	2826	643
4	5337	643

prune190.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	278	6	284

Error

0.1b

Counts

284 → 6

Alt Table

Status	Error	Program
	32.8b	(-.f64 (.f64 (pow.f64 re 3) (+.f64 (.f64 im 1/6) (.f64 (pow.f64 im 3) 1/36))) (.f64 re (fma.f64 (pow.f64 im 3) 1/6 im)))
✓	45.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.9b	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	35.9b	(.f64 (sin.f64 re) (fma.f64 (sqrt.f64 im) (neg.f64 (sqrt.f64 im)) (.f64 (pow.f64 im 3) -1/6)))
▶	20.9b	(.f64 (sin.f64 re) (fma.f64 (cbrt.f64 (.f64 im im)) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))
	47.6b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (.f64 (exp.f64 im) re) -1/2)))

Compiler

Compiled 5580 to 3527 computations (36.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (pow.f64 im 3) -1/6)
✓	0.2b	(fma.f64 (cbrt.f64 (.f64 im im)) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
✓	0.6b	(cbrt.f64 im)
✓	29.6b	(cbrt.f64 (*.f64 im im))

series87.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

31.0ms	(fma.f64 (cbrt.f64 (.f64 im im)) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
28.0ms	(cbrt.f64 (*.f64 im im))
28.0ms	(cbrt.f64 im)

rewrite47.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

757×	`log1p-expm1-u_binary64`
757×	`expm1-log1p-u_binary64`
273×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`

Counts

3 → 86

Calls

3 calls:

45.0ms	(fma.f64 (cbrt.f64 (.f64 im im)) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
45.0ms	(cbrt.f64 im)
45.0ms	(cbrt.f64 (*.f64 im im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	221	17
2	2010	17
3	4984	17
0	0	0
1	0	0

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1634×	`fma-def_binary64`
674×	`fma-neg_binary64`
445×	`unswap-sqr_binary64`
425×	`distribute-rgt-neg-in_binary64`
406×	`sqr-pow_binary64`

Counts

122 → 99

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	22	258
1	60	252
2	124	252
3	337	252
4	953	252
5	1712	252
6	3309	252
7	3666	252
8	4058	252
9	4489	230
10	3969	230
11	4778	230

prune76.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	116	6	122

Error

0.1b

Counts

122 → 6

Alt Table

Status	Error	Program
	32.8b	(-.f64 (.f64 (pow.f64 re 3) (+.f64 (.f64 im 1/6) (.f64 (pow.f64 im 3) 1/36))) (.f64 re (fma.f64 (pow.f64 im 3) 1/6 im)))
✓	45.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.9b	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	35.9b	(.f64 (sin.f64 re) (fma.f64 (sqrt.f64 im) (neg.f64 (sqrt.f64 im)) (.f64 (pow.f64 im 3) -1/6)))
	47.6b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (.f64 (exp.f64 im) re) -1/2)))
▶	8.3b	(.f64 (sin.f64 re) (fma.f64 (sqrt.f64 (.f64 im (cbrt.f64 im))) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 2272 to 1293 computations (43.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 im (cbrt.f64 im))
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 im (cbrt.f64 im))) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
	0.6b	(cbrt.f64 im)
✓	11.6b	(sqrt.f64 (*.f64 im (cbrt.f64 im)))

series128.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

50.0ms	(fma.f64 (sqrt.f64 (.f64 im (cbrt.f64 im))) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
41.0ms	(sqrt.f64 (*.f64 im (cbrt.f64 im)))
36.0ms	(*.f64 im (cbrt.f64 im))

rewrite48.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
299×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
101×	`add-cbrt-cube_binary64`

Counts

3 → 68

Calls

3 calls:

47.0ms	(*.f64 im (cbrt.f64 im))
47.0ms	(fma.f64 (sqrt.f64 (.f64 im (cbrt.f64 im))) (neg.f64 (cbrt.f64 im)) (.f64 (pow.f64 im 3) -1/6))
47.0ms	(sqrt.f64 (*.f64 im (cbrt.f64 im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	226	18
2	2118	18
3	5243	18
0	0	0
1	0	0

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1125×	`fma-neg_binary64`
414×	`distribute-rgt-neg-in_binary64`
402×	`cancel-sign-sub-inv_binary64`
388×	`neg-mul-1_binary64`
377×	`associate-l_binary64`

Counts

104 → 83

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	393
1	77	393
2	193	393
3	544	393
4	1557	393
5	2971	393
6	4553	393
7	4930	393
8	4854	393

prune96.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	163	6	169

Error

0.1b

Counts

169 → 6

Alt Table

Status	Error	Program
	32.8b	(-.f64 (.f64 (pow.f64 re 3) (+.f64 (.f64 im 1/6) (.f64 (pow.f64 im 3) 1/36))) (.f64 re (fma.f64 (pow.f64 im 3) 1/6 im)))
✓	45.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.9b	(.f64 (sin.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	35.9b	(.f64 (sin.f64 re) (fma.f64 (sqrt.f64 im) (neg.f64 (sqrt.f64 im)) (.f64 (pow.f64 im 3) -1/6)))
	47.6b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (.f64 (exp.f64 im) re) -1/2)))
✓	8.3b	(.f64 (sin.f64 re) (fma.f64 (sqrt.f64 (.f64 im (cbrt.f64 im))) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 3219 to 1849 computations (42.6% saved)

regimes206.0ms (2.2%)

Accuracy

Total 0.7b remaining (84.8%)

Threshold costs 0.7b (84.8%)

Counts

37 → 1

Compiler

Compiled 3087 to 2282 computations (26.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	18	15
2	21	15
3	22	15
4	22	15

end99.0ms (1.1%)

Compiler: Compiled 136 to 98 computations (27.9% saved)

Details

analyze1.0s (11.2%)

sample6.4s (70%)

simplify130.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series17.0ms (0.2%)

rewrite61.0ms (0.7%)

simplify73.0ms (0.8%)

prune26.0ms (0.3%)

localize8.0ms (0.1%)

series31.0ms (0.3%)

rewrite102.0ms (1.1%)

simplify53.0ms (0.6%)

prune190.0ms (2.1%)

localize13.0ms (0.1%)

series87.0ms (0.9%)

rewrite47.0ms (0.5%)

simplify124.0ms (1.3%)

prune76.0ms (0.8%)

localize12.0ms (0.1%)

series128.0ms (1.4%)

rewrite48.0ms (0.5%)

simplify90.0ms (1%)

prune96.0ms (1%)

regimes206.0ms (2.2%)

simplify2.0ms (0%)

end99.0ms (1.1%)

Profiling