Details

analyze541.0ms (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%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample4.8s (44.2%)

Results

1.5s	2045×	body	1024	valid
1.1s	1975×	body	1024	invalid
662.0ms	4661×	body	128	valid
468.0ms	1025×	body	512	valid
443.0ms	1036×	body	512	invalid
145.0ms	572×	body	256	invalid
136.0ms	522×	body	256	valid
121.0ms	808×	body	128	invalid
6.0ms	3×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	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 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

series18.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

15.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`fma-def_binary64`
15×	`*-un-lft-identity_binary64`
13×	`exp-sum_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

12.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
10.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
579×	`fma-neg_binary64`
407×	`times-frac_binary64`
388×	`*-commutative_binary64`
341×	`distribute-rgt-in_binary64`

Counts

91 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1574
1	410	1348
2	1452	1317
3	4116	1316
4	5087	1316

prune83.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	4	103

Error

Counts

103 → 4

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
▶	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	29.0b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 2374 to 1327 computations (44.1% saved)

localize15.0ms (0.1%)

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 (exp.f64 (-.f64 0 im)) (exp.f64 im))
✓	0.4b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.4b	(.f64 (.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

series41.0ms (0.4%)

Counts

3 → 56

Calls

3 calls:

23.0ms

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

16.0ms

(*.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

2.0ms

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

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

8.0ms

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

8.0ms

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

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-def_binary64`
450×	`distribute-rgt-in_binary64`
351×	`associate-l_binary64`
337×	`cancel-sign-sub-inv_binary64`
261×	`associate-r_binary64`

Counts

134 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3621
1	672	3081
2	2364	2954
3	4955	2954

prune123.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
✓	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	29.0b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 6213 to 2927 computations (52.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
✓	0.6b	(cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))

series2.8s (26.3%)

Counts

4 → 76

Calls

4 calls:

1.5s	(cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))
1.3s	(.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
22.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
7.0ms	(/.f64 1/2 (exp.f64 im))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`pow1/3_binary64`

Counts

4 → 108

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
4.0ms	(.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
3.0ms	(/.f64 1/2 (exp.f64 im))
2.0ms	(cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

387×	`associate-r_binary64`
348×	`fma-def_binary64`
306×	`times-frac_binary64`
280×	`associate-l_binary64`
233×	`associate-/l*_binary64`

Counts

184 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	448	8110
1	1342	7318
2	5052	7318

prune422.0ms (3.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	357	0	357
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	357	4	361

Error

Counts

361 → 4

Alt Table

Status	Error	Program
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
✓	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	29.0b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 24073 to 14411 computations (40.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	0.0b	(sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

series92.0ms (0.8%)

Counts

2 → 44

Calls

2 calls:

62.0ms

(sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

29.0ms

(*.f64 (sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`pow1_binary64`
74×	`pow-prod-down_binary64`
63×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
16×	`associate-*r/_binary64`

Counts

2 → 92

Calls

2 calls:

28.0ms

(*.f64 (sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

11.0ms

(sqrt.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
271×	`associate-r_binary64`
248×	`distribute-rgt-in_binary64`
243×	`associate-l_binary64`

Counts

136 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	3795
1	564	3070
2	2196	2784
3	4932	2782
4	5109	2782

prune278.0ms (2.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	362	0	362
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	362	4	366

Error

Counts

366 → 4

Alt Table

Status	Error	Program
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))) (cbrt.f64 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)))) (cbrt.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))))
✓	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	29.0b	(.f64 (sqrt.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))) (sqrt.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 13348 to 8193 computations (38.6% saved)

regimes847.0ms (7.8%)

Accuracy

Total 0.0b remaining (21.5%)

Threshold costs 0.0b (21.5%)

Counts

112 → 1

Compiler

Compiled 17505 to 12352 computations (29.4% 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	13	22
1	20	22
2	22	22
3	23	22
4	23	22

end87.0ms (0.8%)

Compiler: Compiled 136 to 97 computations (28.7% saved)

Details

analyze541.0ms (5%)

sample4.8s (44.2%)

simplify74.0ms (0.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series18.0ms (0.2%)

rewrite25.0ms (0.2%)

simplify71.0ms (0.7%)

prune83.0ms (0.8%)

localize15.0ms (0.1%)

series41.0ms (0.4%)

rewrite44.0ms (0.4%)

simplify86.0ms (0.8%)

prune123.0ms (1.1%)

localize10.0ms (0.1%)

series2.8s (26.3%)

rewrite22.0ms (0.2%)

simplify120.0ms (1.1%)

prune422.0ms (3.9%)

localize10.0ms (0.1%)

series92.0ms (0.8%)

rewrite52.0ms (0.5%)

simplify113.0ms (1%)

prune278.0ms (2.6%)

regimes847.0ms (7.8%)

simplify2.0ms (0%)

end87.0ms (0.8%)

Profiling