Details

analyze579.0ms (9.2%)

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
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample116.0ms (1.8%)

Algorithm

1×

intervals

Results

36.0ms	75×	body	1024	valid
29.0ms	64×	body	1024	invalid
11.0ms	142×	body	128	valid
7.0ms	32×	body	512	invalid
6.0ms	80×	body	128	invalid
6.0ms	25×	body	512	valid
3.0ms	23×	body	256	invalid
2.0ms	14×	body	256	valid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`pow1_binary64`
10×	`pow-prod-down_binary64`
8×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`flip3-+_binary64`

Counts

1 → 49

Calls

1 calls:

18.0ms

(*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 1024 to 653 computations (36.2% saved)

series32.0ms (0.5%)

Error

0.0b

Counts

1 → 11

Calls

1 calls:

25.0ms

(*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 536 to 356 computations (33.6% saved)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
495×	`fma-neg_binary64`
359×	`cancel-sign-sub-inv_binary64`
311×	`distribute-rgt-in_binary64`
206×	`associate-l_binary64`

Counts

60 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	1392
1	417	1165
2	1733	1124
3	4569	1124
4	4934	1124

prune27.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	0.2b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
	31.9b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
▶	0.1b	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))

Compiler

Compiled 743 to 404 computations (45.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (exp.f64 im))
0.0b	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))
0.1b	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
0.4b	(log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))

rewrite159.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 143

Calls

4 calls:

14.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))
13.0ms	(/.f64 1/2 (exp.f64 im))
9.0ms	(log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))
9.0ms	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))

Compiler

Compiled 2413 to 1415 computations (41.4% saved)

series262.0ms (4.2%)

Error

Counts

4 → 38

Calls

4 calls:

131.0ms	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
68.0ms	(log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))
29.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))
7.0ms	(/.f64 1/2 (exp.f64 im))

Compiler

Compiled 2566 to 1787 computations (30.4% saved)

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

853×	`times-frac_binary64`
371×	`cancel-sign-sub-inv_binary64`
222×	`unswap-sqr_binary64`
174×	`fma-def_binary64`
172×	`associate-r_binary64`

Counts

181 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	3354
1	664	2979
2	2409	2934
3	5121	2934

prune62.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	0.2b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
	31.9b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))

Compiler

Compiled 1820 to 1024 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
0.2b	(.f64 (sin.f64 re) (.f64 im im))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

2 → 68

Calls

2 calls:

13.0ms	(.f64 (sin.f64 re) (.f64 im im))
10.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

Compiler

Compiled 948 to 302 computations (68.1% saved)

series48.0ms (0.8%)

Error

Counts

2 → 18

Calls

2 calls:

27.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
15.0ms	(.f64 (sin.f64 re) (.f64 im im))

Compiler

Compiled 613 to 443 computations (27.7% saved)

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
506×	`cancel-sign-sub-inv_binary64`
482×	`prod-exp_binary64`
317×	`distribute-rgt-neg-in_binary64`
302×	`*-commutative_binary64`

Counts

86 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	1167
1	263	1050
2	921	975
3	2496	943
4	4072	937
5	5205	937

prune33.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	55	4	59

Error

Counts

59 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	0.2b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
▶	31.9b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))

Compiler

Compiled 660 to 323 computations (51.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))
0.0b	(/.f64 re (exp.f64 im))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 79

Calls

2 calls:

14.0ms	(/.f64 re (exp.f64 im))
9.0ms	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))

Compiler

Compiled 1073 to 323 computations (69.9% saved)

series38.0ms (0.6%)

Error

Counts

2 → 18

Calls

2 calls:

18.0ms	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))
12.0ms	(/.f64 re (exp.f64 im))

Compiler

Compiled 552 to 355 computations (35.7% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

784×	`associate-l_binary64`
736×	`times-frac_binary64`
498×	`fma-neg_binary64`
366×	`fma-def_binary64`
308×	`associate-/l*_binary64`

Counts

97 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	980
1	270	939
2	919	928
3	4947	928
4	5339	928

prune55.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Status	Error	Program
	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	0.2b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
	31.9b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
	0.1b	(expm1.f64 (log1p.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))

Compiler

Compiled 613 to 251 computations (59.1% saved)

regimes315.0ms (5%)

Accuracy

Total 0.0b remaining (19.6%)

Threshold costs 0.0b (19.6%)

Compiler

Compiled 3477 to 2660 computations (23.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub0-neg_binary64`
1×	`sub-neg_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	16	24
2	19	24
3	20	24
4	20	24

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample4.0s (62.8%)

Algorithm

1×

intervals

Results

1.3s	2065×	body	1024	valid
812.0ms	1936×	body	1024	invalid
373.0ms	4504×	body	128	valid
266.0ms	1001×	body	512	invalid
236.0ms	929×	body	512	valid
224.0ms	2574×	body	128	invalid
81.0ms	499×	body	256	invalid
78.0ms	496×	body	256	valid
8.0ms	6×	body	2048	valid

Compiler

Compiled 87 to 62 computations (28.7% saved)

Details

analyze579.0ms (9.2%)

sample116.0ms (1.8%)

simplify83.0ms (1.3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite57.0ms (0.9%)

series32.0ms (0.5%)

simplify75.0ms (1.2%)

prune27.0ms (0.4%)

localize10.0ms (0.2%)

rewrite159.0ms (2.5%)

series262.0ms (4.2%)

simplify96.0ms (1.5%)

prune62.0ms (1%)

localize6.0ms (0.1%)

rewrite57.0ms (0.9%)

series48.0ms (0.8%)

simplify82.0ms (1.3%)

prune33.0ms (0.5%)

localize6.0ms (0.1%)

rewrite53.0ms (0.8%)

series38.0ms (0.6%)

simplify74.0ms (1.2%)

prune55.0ms (0.9%)

regimes315.0ms (5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample4.0s (62.8%)

Profiling