Details

analyze593.0ms (10.8%)

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)

sample101.0ms (1.8%)

Algorithm

1×

intervals

Results

32.0ms	62×	body	1024	valid
23.0ms	65×	body	1024	invalid
10.0ms	140×	body	128	valid
9.0ms	34×	body	512	valid
6.0ms	31×	body	512	invalid
3.0ms	20×	body	256	valid
3.0ms	20×	body	256	invalid
2.0ms	24×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
340×	`associate-/r/_binary64`
318×	`associate-/l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	63	18
3	83	18
4	130	18
5	231	18
6	472	18
7	824	18
8	3187	18
9	3032	18
10	3749	18
11	3945	18
12	4370	18
13	4808	18
14	4906	18
15	4947	18

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.0b

Counts

1 → 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 26 to 20 computations (23.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.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)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

2 → 35

Calls

2 calls:

8.0ms	(.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))

Compiler

Compiled 642 to 207 computations (67.8% saved)

series49.0ms (0.9%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

31.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Compiler

Compiled 768 to 526 computations (31.5% saved)

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

389×	`times-frac_binary64`
362×	`*-commutative_binary64`
355×	`distribute-rgt-in_binary64`
325×	`distribute-lft-in_binary64`
270×	`sub-neg_binary64`

Counts

53 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1232
1	366	1057
2	1267	1026
3	3292	976
4	4774	976
5	4928	976

prune18.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	2	34

Error

Counts

34 → 2

Alt Table

Status	Error	Program
	61.2b	(/.f64 (.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	0.0b	(+.f64 (.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re)) (.f64 (exp.f64 im) (*.f64 1/2 (cos.f64 re))))

Status

Error

Program

61.2b

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

▶

0.0b

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

Compiler

Compiled 537 to 263 computations (51% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re))
0.0b	(+.f64 (.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re)) (.f64 (exp.f64 im) (*.f64 1/2 (cos.f64 re))))
0.0b	(.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re)))
0.0b	(/.f64 1/2 (exp.f64 im))

rewrite79.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
16×	`associate-l_binary64`

Counts

4 → 88

Calls

4 calls:

6.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re))
6.0ms	(+.f64 (.f64 (/.f64 1/2 (exp.f64 im)) (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)))
3.0ms	(/.f64 1/2 (exp.f64 im))

Compiler

Compiled 1933 to 983 computations (49.1% saved)

series107.0ms (2%)

Error

Counts

4 → 42

Calls

4 calls:

35.0ms	(+.f64 (.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re)) (.f64 (exp.f64 im) (*.f64 1/2 (cos.f64 re))))
23.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re))
20.0ms	(.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re)))
8.0ms	(/.f64 1/2 (exp.f64 im))

Compiler

Compiled 1970 to 1267 computations (35.7% saved)

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Rules

602×	`cancel-sign-sub-inv_binary64`
267×	`associate-*l/_binary64`
216×	`associate-r_binary64`
211×	`associate-/l*_binary64`
208×	`associate-l_binary64`

Counts

130 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	2376
1	599	2198
2	1918	2123
3	4278	2118
4	5005	2118

prune46.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	80	2	82

Error

Counts

82 → 2

Alt Table

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

Status

Error

Program

▶

0.4b

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

✓

0.0b

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

Compiler

Compiled 1552 to 810 computations (47.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))) (cos.f64 re)) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
0.0b	(.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re)))
0.0b	(/.f64 (sqrt.f64 1/2) (exp.f64 im))
1.0b	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))

rewrite115.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

51×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

4 → 116

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))
9.0ms	(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))) (cos.f64 re)) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
9.0ms	(/.f64 (sqrt.f64 1/2) (exp.f64 im))
5.0ms	(.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re)))

Compiler

Compiled 2799 to 1714 computations (38.8% saved)

series109.0ms (2%)

Error

Counts

4 → 33

Calls

4 calls:

44.0ms	(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))) (cos.f64 re)) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
20.0ms	(.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re)))
12.0ms	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))
11.0ms	(/.f64 (sqrt.f64 1/2) (exp.f64 im))

Compiler

Compiled 1937 to 1387 computations (28.4% saved)

simplify177.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

414×	`cancel-sign-sub-inv_binary64`
376×	`associate-/l*_binary64`
254×	`associate-r_binary64`
237×	`associate-l_binary64`
201×	`distribute-rgt-neg-in_binary64`

Counts

149 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	236	2885
1	618	2477
2	2063	2417
3	4627	2401
4	4988	2401
5	5000	2401
6	4928	2401

prune52.0ms (0.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	102	2	104

Error

Counts

104 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))) (cos.f64 re)) (.f64 (exp.f64 im) (.f64 1/2 (cos.f64 re))))
	0.0b	(+.f64 (.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re)) (.f64 (exp.f64 im) (*.f64 1/2 (cos.f64 re))))

Status

Error

Program

0.4b

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

0.0b

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

Compiler

Compiled 1789 to 1058 computations (40.9% saved)

regimes246.0ms (4.5%)

Accuracy

Total 0.0b remaining (24.7%)

Threshold costs 0.0b (24.7%)

Compiler

Compiled 4180 to 3113 computations (25.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	15	24

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample3.4s (61.8%)

Algorithm

1×

intervals

Results

1.0s	1996×	body	1024	valid
755.0ms	2042×	body	1024	invalid
387.0ms	4475×	body	128	valid
258.0ms	1038×	body	512	valid
210.0ms	957×	body	512	invalid
113.0ms	485×	body	256	valid
77.0ms	521×	body	256	invalid
70.0ms	724×	body	128	invalid
8.0ms	6×	body	2048	valid

Compiler

Compiled 71 to 50 computations (29.6% saved)

Details

analyze593.0ms (10.8%)

sample101.0ms (1.8%)

simplify121.0ms (2.2%)

prune1.0ms (0%)

localize8.0ms (0.2%)

rewrite36.0ms (0.7%)

series49.0ms (0.9%)

simplify102.0ms (1.9%)

prune18.0ms (0.3%)

localize9.0ms (0.2%)

rewrite79.0ms (1.4%)

series107.0ms (2%)

simplify112.0ms (2%)

prune46.0ms (0.8%)

localize11.0ms (0.2%)

rewrite115.0ms (2.1%)

series109.0ms (2%)

simplify177.0ms (3.2%)

prune52.0ms (0.9%)

regimes246.0ms (4.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.4s (61.8%)

Profiling