Details

analyze492.0ms (2.4%)

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)

sample4.4s (21.7%)

Results

1.4s	2076×	body	1024	valid
1.1s	2001×	body	1024	invalid
645.0ms	4603×	body	128	valid
394.0ms	1056×	body	512	valid
345.0ms	961×	body	512	invalid
142.0ms	515×	body	256	valid
121.0ms	510×	body	256	invalid
107.0ms	707×	body	128	invalid
8.0ms	6×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify111.0ms (0.5%)

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

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%)

Local error

Found 1 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)))

series15.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

15.0ms

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

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 25

Calls

1 calls:

9.0ms

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

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary64`
571×	`fma-def_binary64`
389×	`times-frac_binary64`
350×	`distribute-rgt-in_binary64`
349×	`*-commutative_binary64`

Counts

49 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1187
1	341	1009
2	1284	991
3	3715	991
4	4820	991
5	4982	991

prune29.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	2	53

Error

0.0b

Counts

53 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	1.0b	(.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))))

Status

Error

Program

✓

0.0b

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

▶

1.0b

(*.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))))

Compiler

Compiled 1140 to 500 computations (56.1% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.3b	(.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))))

series46.0ms (0.2%)

Counts

3 → 56

Calls

3 calls:

23.0ms

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

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))))

6.0ms

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

rewrite39.0ms (0.2%)

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:

15.0ms

(*.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))))

12.0ms

(*.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)))

simplify126.0ms (0.6%)

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

prune86.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	176	3	179

Error

Counts

179 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.0b	(.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))))
▶	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))

Compiler

Compiled 5628 to 1916 computations (66% saved)

localize73.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
✓	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
✓	0.7b	(.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
✓	1.0b	(*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

series203.0ms (1%)

Counts

4 → 84

Calls

4 calls:

78.0ms	(.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
71.0ms	(.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
51.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
2.0ms	(*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

rewrite3.9s (19%)

Algorithm

1×	rewrite-expression-head

Rules

5898×	`sqrt-div_binary64`
4408×	`frac-times_binary64`
4171×	`pow1_binary64`
2949×	`flip-+_binary64`
2949×	`flip3-+_binary64`

Counts

4 → 2441

Calls

4 calls:

306.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
281.0ms	(.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
94.0ms	(.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
17.0ms	(*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

simplify6.1s (30%)

Algorithm

1×	egg-herbie

Rules

1047×	`associate-l_binary64`
1031×	`associate-r_binary64`
60×	`fma-def_binary64`
15×	`swap-sqr_binary64`
15×	`sqr-pow_binary64`

Counts

2525 → 3376

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2487	266027
1	5315	266027

prune4.2s (20.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	3449	0	3449
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	3449	3	3452

Error

Counts

3452 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.0b	(.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))))
✓	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 1/2 (cos.f64 re)) (.f64 1/2 (cos.f64 re))) (.f64 1/2 (cos.f64 re))) (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))

Compiler

Compiled 394194 to 103150 computations (73.8% saved)

regimes366.0ms (1.8%)

Accuracy

Total 0.0b remaining (45.2%)

Threshold costs 0.0b (45.2%)

Counts

49 → 1

Compiler

Compiled 13442 to 6218 computations (53.7% 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

end67.0ms (0.3%)

Compiler: Compiled 126 to 63 computations (50% saved)

Details

analyze492.0ms (2.4%)

sample4.4s (21.7%)

simplify111.0ms (0.5%)

prune2.0ms (0%)

localize9.0ms (0%)

series15.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify79.0ms (0.4%)

prune29.0ms (0.1%)

localize10.0ms (0%)

series46.0ms (0.2%)

rewrite39.0ms (0.2%)

simplify126.0ms (0.6%)

prune86.0ms (0.4%)

localize73.0ms (0.4%)

series203.0ms (1%)

rewrite3.9s (19%)

simplify6.1s (30%)

prune4.2s (20.6%)

regimes366.0ms (1.8%)

simplify2.0ms (0%)

end67.0ms (0.3%)

Profiling