Details

analyze1.6s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample163.0ms

Algorithm

intervals

Results

66.0ms	80×	body	1280	invalid
32.0ms	247×	body	80	valid
21.0ms	32×	body	640	invalid
7.0ms	17×	body	320	invalid
4.0ms	2×	body	2560	invalid
2.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	5×	body	160	invalid
1.0ms	8×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify497.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.8b

Counts

2 → 1

localize43.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5128	689

prune131.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Merged error: 19.7b

Counts

69 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
18.6b	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 59

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(* (atan2 x.im x.re) y.re)
39.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5190	596

prune114.0ms

Filtered

53 candidates to 71 candidates (-34.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Merged error: 9.9b

Counts

76 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (neg x.re)) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
18.6b	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
9×	`associate-r`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow`

Counts

4 → 63

Calls

4 calls:

4.0ms	(* (log (neg x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (log (neg x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4924	566
1	4924	566

prune123.0ms

Filtered

50 candidates to 75 candidates (-50.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	70	11	81

Merged error: 9.8b

Counts

81 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.7b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
0.9b	(* (atan2 x.im x.re) y.im)
18.4b	(sin (+ (* (log (neg x.re)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`sin-sum` `pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt y.re)
7.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
3.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt y.re)
28.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5359	526

prune78.0ms

Filtered

46 candidates to 68 candidates (-47.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	7	7
Picked	1	0	1
Done	0	3	3
Total	67	12	79

Merged error: 9.8b

Counts

79 → 12

regimes757.0ms

Accuracy

78.1% (4.5b remaining)

Error of 17.3b against oracle of 12.8b and baseline of 33.5b

bsearch176.0ms

Steps

Iters	Range		Point
7	-7.036436276718186e-307	7.528892925760773e-309	3.9364112129988e-310
10	-493.3232908439566	-4.368127075019549e-09	-0.86023829955213

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	94
1	81	94

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	2122×	body	1280	invalid
929.0ms	7585×	body	80	valid
684.0ms	1283×	body	640	invalid
186.0ms	499×	body	320	invalid
82.0ms	157×	body	640	valid
80.0ms	106×	body	1280	valid
79.0ms	44×	body	2560	invalid
50.0ms	380×	body	80	invalid
39.0ms	99×	body	320	valid
37.0ms	150×	body	160	invalid
13.0ms	53×	body	160	valid

Details

analyze1.6s

sample163.0ms

simplify497.0ms

prune16.0ms

localize43.0ms

rewrite23.0ms

series89.0ms

simplify45.0ms

prune131.0ms

localize25.0ms

rewrite17.0ms

series57.0ms

simplify69.0ms

prune114.0ms

localize20.0ms

rewrite17.0ms

series65.0ms

simplify65.0ms

prune123.0ms

localize24.0ms

rewrite19.0ms

series97.0ms

simplify75.0ms

prune78.0ms

regimes757.0ms

bsearch176.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling