Details

analyze545.0ms (8.5%)

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
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 15 to 12 computations (20% saved)

sample4.8s (75%)

Results

1.5s	2060×	body	1024	valid
1.2s	1926×	body	1024	invalid
777.0ms	4641×	body	128	valid
430.0ms	1053×	body	512	valid
366.0ms	1006×	body	512	invalid
162.0ms	545×	body	256	invalid
129.0ms	496×	body	256	valid
123.0ms	792×	body	128	invalid
8.0ms	6×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify74.0ms (1.2%)

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 (0.1%)

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

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)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 im)
✓	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))

series67.0ms (1%)

Counts

4 → 44

Calls

4 calls:

34.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
23.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
8.0ms	(/.f64 1/2 (exp.f64 im))
1.0ms	(exp.f64 im)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 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))
1.0ms	(exp.f64 im)
0.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
557×	`fma-def_binary64`
509×	`associate-l_binary64`
431×	`associate-r_binary64`
311×	`times-frac_binary64`

Counts

118 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	1929
1	426	1771
2	1254	1747
3	4041	1743
4	5200	1743

prune102.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	151	2	153

Error

Counts

153 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 2685 to 1447 computations (46.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 im)
✓	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)))

series17.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

15.0ms	(.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))

rewrite162.0ms (2.5%)

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:

71.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
8.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify71.0ms (1.1%)

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

prune83.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	123	2	125

Error

Counts

125 → 2

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 2555 to 1429 computations (44.1% saved)

localize6.0ms (0.1%)

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 (0.5%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
11.0ms	(.f64 (sin.f64 re) (.f64 im im))

rewrite6.0ms (0.1%)

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:

5.0ms	(.f64 (sin.f64 re) (.f64 im im))
0.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

simplify83.0ms (1.3%)

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

prune46.0ms (0.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	71	2	73

Error

Counts

73 → 2

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 1247 to 578 computations (53.6% saved)

regimes134.0ms (2.1%)

Accuracy

Total 0.0b remaining (24.4%)

Threshold costs 0.0b (24.4%)

Counts

21 → 1

Compiler

Compiled 1572 to 1154 computations (26.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	18	18
2	20	18
3	21	18
4	21	18

end52.0ms (0.8%)

Compiler: Compiled 52 to 38 computations (26.9% saved)

Details

analyze545.0ms (8.5%)

sample4.8s (75%)

simplify74.0ms (1.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series67.0ms (1%)

rewrite10.0ms (0.1%)

simplify82.0ms (1.3%)

prune102.0ms (1.6%)

localize11.0ms (0.2%)

series17.0ms (0.3%)

rewrite162.0ms (2.5%)

simplify71.0ms (1.1%)

prune83.0ms (1.3%)

localize6.0ms (0.1%)

series29.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify83.0ms (1.3%)

prune46.0ms (0.7%)

regimes134.0ms (2.1%)

simplify2.0ms (0%)

end52.0ms (0.8%)

Profiling