Details

analyze478.0ms (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)

sample4.2s (68.7%)

Results

1.4s	2043×	body	1024	valid
1.1s	2077×	body	1024	invalid
609.0ms	4664×	body	128	valid
384.0ms	1064×	body	512	valid
338.0ms	1008×	body	512	invalid
129.0ms	517×	body	256	invalid
121.0ms	482×	body	256	valid
110.0ms	801×	body	128	invalid
5.0ms	3×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
351×	`fma-def_binary64`
340×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	70	18
3	134	17
4	194	17
5	347	17
6	783	17
7	1356	17
8	3975	17
9	4498	17

Stop Event

1×	node limit

Counts

1 → 2

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 3 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)))
✓	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series19.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

16.0ms	(.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))
1.0ms	(cos.f64 re)

rewrite100.0ms (1.6%)

Algorithm

5×	egg-rewrite
1×	batch-egg-rewrite

Rules

267×	`log1p-expm1-u_binary64`
267×	`expm1-log1p-u_binary64`
245×	`add-cbrt-cube_binary64`
244×	`add-cube-cbrt_binary64`
241×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	233	31
2	3763	31
0	6	10
1	126	10
2	2049	10
0	6	10
0	11	18
1	233	18
2	3740	18
0	11	18
0	3	3
1	58	3
2	679	3

Stop Event

1×	node limit
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 52

Calls

3 calls:

99.0ms	(cos.f64 re)
99.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
99.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
476×	`fma-def_binary64`
279×	`sub-neg_binary64`
212×	`distribute-rgt-neg-in_binary64`
204×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	724
1	246	666
2	773	642
3	3310	642

Stop Event

1×	node limit

Counts

88 → 86

prune58.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Error

Counts

87 → 4

Alt Table

Status	Error	Program
▶	1.0b	(log.f64 (exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
	59.3b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
	1.2b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 1683 to 790 computations (53.1% saved)

localize11.0ms (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	(*.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.1b	(exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
✓	0.3b	(log.f64 (exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))

series49.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

23.0ms

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

14.0ms

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

11.0ms

(*.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite106.0ms (1.7%)

Algorithm

6×	egg-rewrite
1×	batch-egg-rewrite

Rules

127×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`
118×	`add-cbrt-cube_binary64`
118×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	255	56
2	3971	56
0	13	18
1	255	18
2	3971	18
0	13	18
0	12	20
1	250	20
2	3960	20
0	12	20
0	9	15
1	190	15
2	3165	15
0	9	15

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 28

Calls

3 calls:

106.0ms

(*.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

106.0ms

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

106.0ms

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

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

657×	`cancel-sign-sub-inv_binary64`
352×	`distribute-rgt-out_binary64`
328×	`associate-r_binary64`
313×	`fma-def_binary64`
224×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	2515
1	770	2186
2	2938	2079

Stop Event

1×	node limit

Counts

100 → 80

prune84.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Error

Counts

104 → 4

Alt Table

Status	Error	Program
✓	1.0b	(log.f64 (exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
	59.3b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.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)))
▶	1.2b	(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))

Compiler

Compiled 3088 to 1506 computations (51.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

17.0ms	(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))
9.0ms	(.f64 im (.f64 im (cos.f64 re)))
8.0ms	(*.f64 im (cos.f64 re))

rewrite42.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
89×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	160	30
2	1883	30

Stop Event

1×	node limit

Counts

3 → 53

Calls

3 calls:

40.0ms	(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))
40.0ms	(.f64 im (.f64 im (cos.f64 re)))
40.0ms	(*.f64 im (cos.f64 re))

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

340×	`fma-def_binary64`
322×	`distribute-rgt-neg-in_binary64`
318×	`sub-neg_binary64`
309×	`distribute-lft-neg-in_binary64`
269×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	918
1	186	904
2	647	823
3	3254	818

Stop Event

1×	node limit

Counts

125 → 84

prune134.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	1.0b	(log.f64 (exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
▶	59.3b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.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)))
✓	1.2b	(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))

Compiler

Compiled 2749 to 1338 computations (51.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 im) (exp.f64 im))
✓	0.3b	(/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	5.9b	(-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im)))
✓	6.0b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series35.0ms (0.6%)

Counts

4 → 44

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
9.0ms	(-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im)))
3.0ms	(*.f64 (exp.f64 im) (exp.f64 im))
2.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite146.0ms (2.4%)

Algorithm

6×	egg-rewrite
1×	batch-egg-rewrite

Rules

1017×	`prod-diff_binary64`
921×	`expm1-log1p-u_binary64`
401×	`log1p-expm1-u_binary64`
365×	`add-log-exp_binary64`
357×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	236	40
2	4264	40
0	6	10
1	127	10
2	2077	10
0	6	10
0	8	16
1	180	14
2	2643	8
0	10	28
1	236	28
2	4375	28
0	10	28
0	4	6
1	77	6
2	883	6

Stop Event

1×	node limit
1×	iter limit
1×	unsound
1×	node limit
1×	iter limit
1×	unsound
1×	unsound

Counts

4 → 108

Calls

4 calls:

144.0ms	(*.f64 (exp.f64 im) (exp.f64 im))
144.0ms	(/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
144.0ms	(-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im)))
144.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
556×	`cancel-sign-sub-inv_binary64`
363×	`fma-def_binary64`
220×	`times-frac_binary64`
125×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	652
1	229	642
2	656	596
3	2340	492

Stop Event

1×	node limit

Counts

152 → 145

prune63.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
✓	1.0b	(log.f64 (exp.f64 (.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
✓	59.3b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (.f64 (exp.f64 im) (exp.f64 im))) (-.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)))
✓	1.2b	(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))

Compiler

Compiled 3907 to 1412 computations (63.9% saved)

regimes253.0ms (4.1%)

Accuracy

Total 0.0b remaining (40.2%)

Threshold costs 0.0b (40.2%)

Counts

44 → 1

Compiler

Compiled 4220 to 2966 computations (29.7% saved)

simplify12.0ms (0.2%)

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

Stop Event

1×

saturated

end70.0ms (1.1%)

Compiler: Compiled 93 to 63 computations (32.3% saved)

Details

analyze478.0ms (7.8%)

sample4.2s (68.7%)

simplify35.0ms (0.6%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series19.0ms (0.3%)

rewrite100.0ms (1.6%)

simplify42.0ms (0.7%)

prune58.0ms (0.9%)

localize11.0ms (0.2%)

series49.0ms (0.8%)

rewrite106.0ms (1.7%)

simplify54.0ms (0.9%)

prune84.0ms (1.4%)

localize6.0ms (0.1%)

series34.0ms (0.6%)

rewrite42.0ms (0.7%)

simplify41.0ms (0.7%)

prune134.0ms (2.2%)

localize13.0ms (0.2%)

series35.0ms (0.6%)

rewrite146.0ms (2.4%)

simplify34.0ms (0.5%)

prune63.0ms (1%)

regimes253.0ms (4.1%)

simplify12.0ms (0.2%)

end70.0ms (1.1%)

Profiling