Details

analyze634.0ms (12.5%)

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%	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)

sample100.0ms (2%)

Algorithm

1×

intervals

Results

34.0ms	72×	body	1024	valid
22.0ms	55×	body	1024	invalid
10.0ms	145×	body	128	valid
6.0ms	29×	body	512	invalid
5.0ms	21×	body	512	valid
3.0ms	22×	body	256	invalid
2.0ms	17×	body	256	valid
2.0ms	25×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify113.0ms (2.2%)

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

prune2.0ms (0%)

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

series20.0ms (0.4%)

Counts

2 → 32

Calls

2 calls:

17.0ms	(.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))

rewrite82.0ms (1.6%)

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:

76.0ms	(.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))

simplify70.0ms (1.4%)

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 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1507
1	387	1292
2	1386	1265
3	3915	1265
4	5044	1265

prune59.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	0.9b	(.f64 (.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (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))

Compiler

Compiled 1637 to 710 computations (56.6% saved)

localize10.0ms (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))
✓	0.4b	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)

series132.0ms (2.6%)

Counts

4 → 76

Calls

4 calls:

70.0ms	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)
28.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
28.0ms	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3))
6.0ms	(/.f64 1/2 (exp.f64 im))

rewrite16.0ms (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:

5.0ms	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re)) 3)
3.0ms	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
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))

simplify98.0ms (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

prune121.0ms (2.4%)

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)))
▶	0.9b	(.f64 (.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (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))

Compiler

Compiled 3978 to 2423 computations (39.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
✓	0.0b	(sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.2b	(.f64 (.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
✓	0.7b	(.f64 (.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

series50.0ms (1%)

Counts

3 → 56

Calls

3 calls:

25.0ms

(*.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

18.0ms

(*.f64 (*.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

7.0ms

(sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
16×	`sqrt-div_binary64`
14×	`associate-r_binary64`

Counts

3 → 80

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

8.0ms

(*.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

4.0ms

(sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
364×	`distribute-rgt-in_binary64`
350×	`cancel-sign-sub-inv_binary64`
344×	`associate-l_binary64`
269×	`fma-neg_binary64`

Counts

136 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	3676
1	674	3248
2	2437	3124
3	4905	3122
4	4966	3122

prune107.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	233	3	236

Error

Counts

236 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.9b	(.f64 (.f64 (*.f64 1/2 (cos.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (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))

Compiler

Compiled 6948 to 2334 computations (66.4% saved)

regimes194.0ms (3.8%)

Accuracy

Total 0.0b remaining (58.7%)

Threshold costs 0.0b (58.7%)

Counts

26 → 1

Compiler

Compiled 2522 to 1862 computations (26.2% 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 (60.8%)

Algorithm

1×

intervals

Results

936.0ms	1975×	body	1024	valid
702.0ms	1977×	body	1024	invalid
318.0ms	4546×	body	128	valid
224.0ms	969×	body	512	valid
197.0ms	952×	body	512	invalid
109.0ms	498×	body	256	invalid
78.0ms	505×	body	256	valid
60.0ms	726×	body	128	invalid
5.0ms	5×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 80 to 57 computations (28.8% saved)

Details

analyze634.0ms (12.5%)

sample100.0ms (2%)

simplify113.0ms (2.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series20.0ms (0.4%)

rewrite82.0ms (1.6%)

simplify70.0ms (1.4%)

prune59.0ms (1.2%)

localize10.0ms (0.2%)

series132.0ms (2.6%)

rewrite16.0ms (0.3%)

simplify98.0ms (1.9%)

prune121.0ms (2.4%)

localize10.0ms (0.2%)

series50.0ms (1%)

rewrite36.0ms (0.7%)

simplify121.0ms (2.4%)

prune107.0ms (2.1%)

regimes194.0ms (3.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.1s (60.8%)

Profiling