Details

analyze485.0ms (8.9%)

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%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample4.3s (78.5%)

Results

1.3s	2053×	body	1024	valid
1.0s	1952×	body	1024	invalid
620.0ms	4647×	body	128	valid
376.0ms	1037×	body	512	invalid
372.0ms	1032×	body	512	valid
145.0ms	553×	body	256	invalid
123.0ms	519×	body	256	valid
106.0ms	735×	body	128	invalid
8.0ms	5×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify115.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
533×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
354×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	65	18
3	99	17
4	154	17
5	269	17
6	532	17
7	916	17
8	3332	17
9	3260	17
10	4006	17
11	4265	17
12	4692	17
13	4840	17
14	4891	17
15	4917	17

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
▶	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 76 to 53 computations (30.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series18.0ms (0.3%)

Counts

2 → 32

Calls

2 calls:

16.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`associate-r_binary64`

Counts

2 → 42

Calls

2 calls:

8.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
4.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-def_binary64`
445×	`fma-neg_binary64`
389×	`times-frac_binary64`
362×	`*-commutative_binary64`
355×	`distribute-rgt-in_binary64`

Counts

74 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1507
1	389	1292
2	1387	1265
3	3915	1265
4	5044	1265

prune52.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 1635 to 688 computations (57.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(/.f64 1/2 (exp.f64 im))

series36.0ms (0.7%)

Counts

3 → 40

Calls

3 calls:

23.0ms	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
7.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
6.0ms	(/.f64 1/2 (exp.f64 im))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

3.0ms	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
3.0ms	(/.f64 1/2 (exp.f64 im))
0.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-neg_binary64`
494×	`associate-l_binary64`
433×	`fma-def_binary64`
422×	`associate-r_binary64`
335×	`times-frac_binary64`

Counts

101 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	1806
1	378	1669
2	1142	1633
3	3806	1629
4	5000	1629
5	5148	1629

prune75.0ms (1.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	107	2	109

Error

Counts

109 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 1975 to 1087 computations (45% saved)

regimes126.0ms (2.3%)

Accuracy

Total 0.0b remaining (16.4%)

Threshold costs 0.0b (16.4%)

Counts

14 → 1

Compiler

Compiled 1069 to 810 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
2	10	17

end50.0ms (0.9%)

Compiler: Compiled 52 to 37 computations (28.8% saved)

Details

analyze485.0ms (8.9%)

sample4.3s (78.5%)

simplify115.0ms (2.1%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series18.0ms (0.3%)

rewrite14.0ms (0.3%)

simplify71.0ms (1.3%)

prune52.0ms (0.9%)

localize8.0ms (0.2%)

series36.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify105.0ms (1.9%)

prune75.0ms (1.4%)

regimes126.0ms (2.3%)

simplify2.0ms (0%)

end50.0ms (0.9%)

Profiling