Details

analyze539.0ms (6.3%)

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)

sample4.7s (54.5%)

Results

1.5s	2101×	body	1024	valid
1.2s	1999×	body	1024	invalid
705.0ms	4625×	body	128	valid
396.0ms	1027×	body	512	valid
380.0ms	1042×	body	512	invalid
140.0ms	484×	body	256	invalid
130.0ms	500×	body	256	valid
108.0ms	693×	body	128	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify114.0ms (1.3%)

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%)

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 (0.1%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.2%)

Counts

3 → 36

Calls

3 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))
2.0ms	(cos.f64 re)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 51

Calls

3 calls:

7.0ms	(.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))
1.0ms	(cos.f64 re)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
529×	`fma-neg_binary64`
357×	`distribute-rgt-in_binary64`
325×	`distribute-lft-in_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

87 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1623
1	422	1397
2	1479	1366
3	4475	1366
4	4993	1366
5	4917	1366

prune87.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

0.0b

Counts

98 → 3

Alt Table

Status	Error	Program
	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
▶	0.0b	(+.f64 (.f64 (exp.f64 (neg.f64 im)) (.f64 1/2 (cos.f64 re))) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
	15.6b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))

Compiler

Compiled 1960 to 868 computations (55.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series47.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

24.0ms

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

12.0ms

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

12.0ms

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

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`pow1_binary64`
9×	`add-exp-log_binary64`
6×	`associate-l_binary64`
6×	`cbrt-unprod_binary64`

Counts

3 → 57

Calls

3 calls:

9.0ms

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

9.0ms

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

5.0ms

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

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
491×	`cancel-sign-sub-inv_binary64`
363×	`distribute-rgt-out_binary64`
336×	`times-frac_binary64`
260×	`associate-r_binary64`

Counts

129 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2334
1	528	2082
2	2045	2038
3	4380	2029
4	5384	2029

prune185.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Error

0.0b

Counts

175 → 3

Alt Table

Status	Error	Program
	0.5b	(log.f64 (.f64 (exp.f64 (.f64 (exp.f64 (neg.f64 im)) (.f64 1/2 (cos.f64 re)))) (exp.f64 (.f64 (exp.f64 im) (*.f64 1/2 (cos.f64 re))))))
✓	0.0b	(+.f64 (.f64 (exp.f64 (neg.f64 im)) (.f64 1/2 (cos.f64 re))) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
▶	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))

Compiler

Compiled 4008 to 2008 computations (49.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 im im))
✓	0.0b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
✓	0.1b	(*.f64 1/24 (pow.f64 im 4))
✓	0.1b	(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4))))

series71.0ms (0.8%)

Counts

4 → 60

Calls

4 calls:

35.0ms	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
30.0ms	(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4))))
3.0ms	(*.f64 1/24 (pow.f64 im 4))
3.0ms	(.f64 1/2 (.f64 im im))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`

Counts

4 → 90

Calls

4 calls:

10.0ms	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
7.0ms	(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4))))
4.0ms	(.f64 1/2 (.f64 im im))
4.0ms	(*.f64 1/24 (pow.f64 im 4))

simplify117.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

599×	`distribute-rgt-in_binary64`
546×	`cancel-sign-sub-inv_binary64`
498×	`fma-neg_binary64`
235×	`associate-r_binary64`
221×	`associate-l_binary64`

Counts

150 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	2882
1	559	2756
2	2188	2678
3	4681	2675
4	4999	2675

prune164.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	156	3	159

Error

0.0b

Counts

159 → 3

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
▶	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 im im)))) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.0b	(+.f64 (.f64 (exp.f64 (neg.f64 im)) (.f64 1/2 (cos.f64 re))) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))

Compiler

Compiled 4193 to 2542 computations (39.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 im im)))) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.1b	(.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 im im)))) (*.f64 1/24 (pow.f64 im 4))))
	0.1b	(*.f64 1/24 (pow.f64 im 4))
✓	3.4b	(log.f64 (sqrt.f64 (exp.f64 (*.f64 im im))))

series1.3s (14.8%)

Counts

3 → 60

Calls

3 calls:

573.0ms

(+.f64 (cos.f64 re) (*.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 im im)))) (*.f64 1/24 (pow.f64 im 4)))))

384.0ms

(*.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 im im)))) (*.f64 1/24 (pow.f64 im 4))))

317.0ms

(log.f64 (sqrt.f64 (exp.f64 (*.f64 im im))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64`

Counts

3 → 63

Calls

3 calls:

7.0ms

(*.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 im im)))) (*.f64 1/24 (pow.f64 im 4))))

4.0ms

(+.f64 (cos.f64 re) (*.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 im im)))) (*.f64 1/24 (pow.f64 im 4)))))

2.0ms

(log.f64 (sqrt.f64 (exp.f64 (*.f64 im im))))

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

586×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
461×	`cancel-sign-sub-inv_binary64`
296×	`fma-neg_binary64`
177×	`fma-def_binary64`

Counts

123 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	3075
1	472	2926
2	1792	2850
3	4651	2521
4	5026	2521

prune182.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	167	3	170

Error

0.0b

Counts

170 → 3

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/24 (pow.f64 im 4)))))
✓	0.4b	(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 im im)))) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.0b	(+.f64 (.f64 (exp.f64 (neg.f64 im)) (.f64 1/2 (cos.f64 re))) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))

Compiler

Compiled 4619 to 2517 computations (45.5% saved)

regimes571.0ms (6.6%)

Accuracy

Total 0.0b remaining (56.6%)

Threshold costs 0.0b (56.6%)

Counts

98 → 1

Compiler

Compiled 9732 to 7119 computations (26.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	22	18
2	24	18
3	25	18
4	24	18

end72.0ms (0.8%)

Compiler: Compiled 83 to 60 computations (27.7% saved)

Details

analyze539.0ms (6.3%)

sample4.7s (54.5%)

simplify114.0ms (1.3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series21.0ms (0.2%)

rewrite15.0ms (0.2%)

simplify99.0ms (1.1%)

prune87.0ms (1%)

localize10.0ms (0.1%)

series47.0ms (0.5%)

rewrite25.0ms (0.3%)

simplify121.0ms (1.4%)

prune185.0ms (2.1%)

localize10.0ms (0.1%)

series71.0ms (0.8%)

rewrite30.0ms (0.3%)

simplify117.0ms (1.4%)

prune164.0ms (1.9%)

localize12.0ms (0.1%)

series1.3s (14.8%)

rewrite17.0ms (0.2%)

simplify118.0ms (1.4%)

prune182.0ms (2.1%)

regimes571.0ms (6.6%)

simplify3.0ms (0%)

end72.0ms (0.8%)

Profiling