Details

analyze1.8s (10.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	96.8%	3.2%	7
0%	95.2%	4.8%	8
0%	92.9%	7.1%	9
0%	91.7%	8.3%	10
0%	90.3%	9.7%	11
0%	89.7%	10.3%	12
0%	88.9%	11.1%	13
0%	88.6%	11.4%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample14.7s (84.6%)

Results

10.8s	4074×	body	8192	exit
1.5s	2087×	body	1024	valid
747.0ms	4623×	body	128	valid
617.0ms	1041×	body	1024	invalid
474.0ms	1026×	body	512	valid
212.0ms	550×	body	512	invalid
141.0ms	518×	body	256	valid
72.0ms	415×	body	128	invalid
69.0ms	252×	body	256	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify76.0ms (0.4%)

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 → 2

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

prune4.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 79 to 56 computations (29.1% saved)

localize8.0ms (0%)

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

series39.0ms (0.2%)

Counts

3 → 40

Calls

3 calls:

25.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
8.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
6.0ms	(/.f64 1/2 (exp.f64 im))

rewrite10.0ms (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 (sin.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)))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
500×	`associate-l_binary64`
496×	`fma-def_binary64`
422×	`associate-r_binary64`
311×	`times-frac_binary64`

Counts

101 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	1824
1	395	1671
2	1184	1647
3	3869	1643
4	5027	1643

prune85.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	0.6b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 2058 to 1136 computations (44.8% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

17.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`fma-def_binary64`
15×	`*-un-lft-identity_binary64`
13×	`exp-sum_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

11.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
9.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
579×	`fma-neg_binary64`
407×	`times-frac_binary64`
388×	`*-commutative_binary64`
341×	`distribute-rgt-in_binary64`

Counts

91 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1574
1	410	1348
2	1452	1317
3	4116	1316
4	5087	1316

prune72.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	102	3	105

Error

Counts

105 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	0.6b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 2227 to 1226 computations (44.9% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.1b	(.f64 (sin.f64 re) (.f64 im im))

series29.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
12.0ms	(.f64 (sin.f64 re) (.f64 im im))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

6.0ms	(.f64 (sin.f64 re) (.f64 im im))
0.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-l_binary64`
408×	`fma-def_binary64`
381×	`associate-r_binary64`
338×	`distribute-rgt-neg-in_binary64`
328×	`distribute-lft-neg-in_binary64`

Counts

79 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1249
1	247	1133
2	809	1043
3	3073	1043
4	4999	1043
5	4930	1043

prune48.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	71	3	74

Error

Counts

74 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	0.6b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 1260 to 587 computations (53.4% saved)

regimes128.0ms (0.7%)

Accuracy

Total 0.0b remaining (22.1%)

Threshold costs 0.0b (22.1%)

Counts

21 → 1

Compiler

Compiled 1584 to 1146 computations (27.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-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	18
1	17	18
2	20	18
3	21	18
4	21	18

end54.0ms (0.3%)

Compiler: Compiled 65 to 47 computations (27.7% saved)

Details

analyze1.8s (10.5%)

sample14.7s (84.6%)

simplify76.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0%)

series39.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify77.0ms (0.4%)

prune85.0ms (0.5%)

localize9.0ms (0%)

series19.0ms (0.1%)

rewrite24.0ms (0.1%)

simplify73.0ms (0.4%)

prune72.0ms (0.4%)

localize6.0ms (0%)

series29.0ms (0.2%)

rewrite8.0ms (0%)

simplify78.0ms (0.5%)

prune48.0ms (0.3%)

regimes128.0ms (0.7%)

simplify2.0ms (0%)

end54.0ms (0.3%)

Profiling