Details

analyze562.0ms (7.8%)

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 (65.2%)

Results

1.6s	2045×	body	1024	valid
1.1s	2020×	body	1024	invalid
708.0ms	4728×	body	128	valid
381.0ms	1008×	body	512	valid
380.0ms	1005×	body	512	invalid
140.0ms	544×	body	256	invalid
119.0ms	469×	body	256	valid
110.0ms	710×	body	128	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify122.0ms (1.7%)

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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

2.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
2.0ms	(cos.f64 re)

rewrite108.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite
2×	egg-rewrite

Rules

444×	`log1p-udef_binary64`
250×	`log1p-expm1-u_binary64`
250×	`expm1-log1p-u_binary64`
231×	`add-cbrt-cube_binary64`
230×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

107.0ms	(cos.f64 re)
107.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	164	13
2	83	13
0	6	10
1	126	10
2	79	10
0	3	3
1	58	3
2	655	3
3	4733	3
4	5597	3
0	0	0
1	0	0

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1019×	`fma-neg_binary64`
780×	`cancel-sign-sub-inv_binary64`
574×	`unswap-sqr_binary64`
394×	`associate-l_binary64`
387×	`fma-def_binary64`

Counts

45 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	139
1	93	133
2	210	125
3	582	123
4	1952	123
5	4875	123
6	4987	123
7	4963	123

prune38.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	2	50

Error

0.0b

Counts

50 → 2

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 1/2 (cos.f64 re)) (fma.f64 im im 2))
▶	0.1b	(.f64 (.f64 1/2 (expm1.f64 (log1p.f64 (cos.f64 re)))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 859 to 433 computations (49.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 re)
	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
✓	0.1b	(expm1.f64 (log1p.f64 (cos.f64 re)))
✓	0.2b	(log1p.f64 (cos.f64 re))

series201.0ms (2.8%)

Counts

2 → 24

Calls

2 calls:

199.0ms	(log1p.f64 (cos.f64 re))
2.0ms	(expm1.f64 (log1p.f64 (cos.f64 re)))

rewrite85.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

576×	`log1p-udef_binary64`
325×	`expm1-log1p-u_binary64`
324×	`log1p-expm1-u_binary64`
291×	`add-log-exp_binary64`
290×	`add-exp-log_binary64`

Counts

2 → 72

Calls

2 calls:

83.0ms	(expm1.f64 (log1p.f64 (cos.f64 re)))
83.0ms	(log1p.f64 (cos.f64 re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	77	8
2	848	8
3	4634	8
4	5822	8
0	0	0
1	0	0

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

635×	`distribute-rgt-neg-in_binary64`
547×	`distribute-lft-neg-in_binary64`
519×	`fma-def_binary64`
426×	`associate-l_binary64`
365×	`associate-r_binary64`

Counts

96 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	180
1	93	176
2	232	170
3	694	166
4	2549	166
5	4650	166
6	4971	166
7	4934	166

prune84.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 1/2 (cos.f64 re)) (fma.f64 im im 2))
▶	0.8b	(.f64 (.f64 1/2 (expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.1b	(.f64 (.f64 1/2 (expm1.f64 (log1p.f64 (cos.f64 re)))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 2609 to 1266 computations (51.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))
	0.2b	(log1p.f64 (cos.f64 re))
✓	0.2b	(+.f64 1 (log1p.f64 (cos.f64 re)))
✓	0.8b	(-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1)

series402.0ms (5.6%)

Counts

3 → 36

Calls

3 calls:

206.0ms	(-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1)
194.0ms	(+.f64 1 (log1p.f64 (cos.f64 re)))
2.0ms	(expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))

rewrite81.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

688×	`expm1-log1p-u_binary64`
687×	`log1p-expm1-u_binary64`
268×	`prod-diff_binary64`
187×	`fma-udef_binary64`
144×	`fma-neg_binary64`

Counts

3 → 109

Calls

3 calls:

79.0ms	(expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))
79.0ms	(+.f64 1 (log1p.f64 (cos.f64 re)))
79.0ms	(-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	169	16
2	1642	16
3	4902	16
4	4944	16
0	0	0
1	0	0

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
635×	`distribute-rgt-neg-in_binary64`
547×	`distribute-lft-neg-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
426×	`associate-l_binary64`

Counts

145 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	316
1	109	312
2	278	304
3	837	296
4	3120	296
5	4835	296
6	5131	296

prune107.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	175	3	178

Error

Counts

178 → 3

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 1/2 (cos.f64 re)) (fma.f64 im im 2))
✓	0.8b	(.f64 (.f64 1/2 (expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.1b	(.f64 (.f64 1/2 (expm1.f64 (log1p.f64 (cos.f64 re)))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 3929 to 2105 computations (46.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite45.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
159×	`log1p-udef_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-log-exp_binary64`

Counts

1 → 17

Calls

1 calls:

44.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	181	13
2	1998	13
3	4941	13
0	0	0
1	0	0

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary64`
578×	`associate--r+_binary64`
354×	`associate-+l-_binary64`
279×	`associate-+r-_binary64`
235×	`sub-neg_binary64`

Counts

41 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	448
1	127	409
2	419	388
3	1731	382
4	4995	382
5	4999	382
6	4966	382

prune56.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	71	3	74

Error

Counts

74 → 3

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (.f64 1/2 (cos.f64 re)) (fma.f64 im im 2))
✓	0.8b	(.f64 (.f64 1/2 (expm1.f64 (-.f64 (+.f64 1 (log1p.f64 (cos.f64 re))) 1))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.1b	(.f64 (.f64 1/2 (expm1.f64 (log1p.f64 (cos.f64 re)))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 1131 to 751 computations (33.6% saved)

regimes163.0ms (2.3%)

Accuracy

Total 0.0b remaining (25.2%)

Threshold costs 0.0b (25.2%)

Counts

26 → 1

Compiler

Compiled 2258 to 1808 computations (19.9% 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

end65.0ms (0.9%)

Compiler: Compiled 71 to 56 computations (21.1% saved)

Details

analyze562.0ms (7.8%)

sample4.7s (65.2%)

simplify122.0ms (1.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series4.0ms (0.1%)

rewrite108.0ms (1.5%)

simplify72.0ms (1%)

prune38.0ms (0.5%)

localize11.0ms (0.2%)

series201.0ms (2.8%)

rewrite85.0ms (1.2%)

simplify90.0ms (1.3%)

prune84.0ms (1.2%)

localize19.0ms (0.3%)

series402.0ms (5.6%)

rewrite81.0ms (1.1%)

simplify79.0ms (1.1%)

prune107.0ms (1.5%)

localize6.0ms (0.1%)

series17.0ms (0.2%)

rewrite45.0ms (0.6%)

simplify68.0ms (1%)

prune56.0ms (0.8%)

regimes163.0ms (2.3%)

simplify2.0ms (0%)

end65.0ms (0.9%)

Profiling