Details

analyze473.0ms (9.9%)

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)

sample236.0ms (4.9%)

Algorithm

1×

intervals

Results

28.0ms	64×	body	1024	valid
23.0ms	63×	body	1024	invalid
9.0ms	142×	body	128	valid
7.0ms	33×	body	512	valid
6.0ms	33×	body	512	invalid
2.0ms	16×	body	256	valid
2.0ms	23×	body	128	invalid
1.0ms	11×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify122.0ms (2.5%)

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

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

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 50 to 35 computations (30% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.4%)

Counts

2 → 28

Calls

2 calls:

17.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(cos.f64 re)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

7.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	(cos.f64 re)

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-neg_binary64`
609×	`fma-def_binary64`
394×	`times-frac_binary64`
365×	`*-commutative_binary64`
352×	`distribute-rgt-in_binary64`

Counts

62 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1303
1	376	1114
2	1377	1092
3	3927	1092
4	4960	1092
5	5054	1092

prune49.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	0.3b	(fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (cos.f64 re))
▶	0.3b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))

Compiler

Compiled 1436 to 643 computations (55.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
✓	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.3b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))
✓	0.3b	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)

series130.0ms (2.7%)

Counts

4 → 76

Calls

4 calls:

73.0ms	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)
26.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
24.0ms	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))
7.0ms	(/.f64 1/2 (exp.f64 im))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`

Counts

4 → 92

Calls

4 calls:

3.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
3.0ms	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)
3.0ms	(/.f64 1/2 (exp.f64 im))
1.0ms	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))

simplify93.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

371×	`cancel-sign-sub-inv_binary64`
286×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
210×	`fma-def_binary64`
170×	`associate-r_binary64`

Counts

168 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	3836
1	632	3671
2	2348	3607
3	5014	3607

prune129.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	156	3	159

Error

Counts

159 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	0.3b	(fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (cos.f64 re))
✓	0.3b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))

Compiler

Compiled 3958 to 2413 computations (39% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (cos.f64 re))
11.0ms	(.f64 (cos.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:

4.0ms	(.f64 (cos.f64 re) (.f64 im im))
0.0ms	(fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (cos.f64 re))

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
435×	`associate-l_binary64`
358×	`associate-r_binary64`
292×	`fma-def_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

79 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1231
1	223	1130
2	712	1039
3	2705	1033
4	4921	1033
5	4959	1033

prune76.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.3b	(fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (cos.f64 re))
✓	0.3b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))

Compiler

Compiled 1770 to 789 computations (55.4% saved)

regimes123.0ms (2.6%)

Accuracy

Total 0.0b remaining (54.8%)

Threshold costs 0.0b (54.8%)

Counts

21 → 1

Compiler

Compiled 1634 to 1172 computations (28.3% saved)

simplify3.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample3.1s (64.7%)

Algorithm

1×

intervals

Results

957.0ms	2006×	body	1024	valid
682.0ms	1933×	body	1024	invalid
327.0ms	4528×	body	128	valid
232.0ms	955×	body	512	valid
192.0ms	962×	body	512	invalid
89.0ms	718×	body	128	invalid
74.0ms	505×	body	256	valid
63.0ms	449×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 70 to 52 computations (25.7% saved)

Details

analyze473.0ms (9.9%)

sample236.0ms (4.9%)

simplify122.0ms (2.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series19.0ms (0.4%)

rewrite9.0ms (0.2%)

simplify82.0ms (1.7%)

prune49.0ms (1%)

localize9.0ms (0.2%)

series130.0ms (2.7%)

rewrite15.0ms (0.3%)

simplify93.0ms (1.9%)

prune129.0ms (2.7%)

localize6.0ms (0.1%)

series28.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify74.0ms (1.5%)

prune76.0ms (1.6%)

regimes123.0ms (2.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.1s (64.7%)

Profiling