Details

analyze1.5s

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

sample140.0ms

Algorithm

intervals

Results

43.0ms	53×	body	1280	invalid
29.0ms	239×	body	80	valid
18.0ms	34×	body	640	invalid
7.0ms	5×	body	1280	valid
6.0ms	16×	body	320	invalid
3.0ms	11×	body	160	invalid
3.0ms	2×	body	2560	invalid
3.0ms	5×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	11×	body	80	invalid
0.0ms	1×	body	160	valid

simplify517.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4970	36
1	4970	36

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4750	692
1	4750	692

prune150.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 18.6b

Counts

70 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.0b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sin-sum`

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
128.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4911	911
1	4911	911

prune161.0ms

Filtered

54 candidates to 61 candidates (-13.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 18.5b

Counts

70 → 10

localize38.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
32.0b	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
10.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
129.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5012	910

prune184.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	66	10	76

Merged error: 18.4b

Counts

76 → 10

localize45.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3)))
32.1b	(sin (+ (* (log (* (fabs (pow (pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3)))
10.0ms	(sin (+ (* (log (* (fabs (pow (pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3)))
157.0ms	(sin (+ (* (log (* (fabs (pow (pow (+ (* x.re x.re) (* x.im x.im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4883	1101
1	4883	1101

prune207.0ms

Filtered

56 candidates to 63 candidates (-12.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	60	13	73

Merged error: 18.4b

Counts

73 → 13

regimes581.0ms

Accuracy

77.5% (3.2b remaining)

Error of 22.3b against oracle of 19.1b and baseline of 33.3b

bsearch1.6s

Steps

Iters	Range		Point
10	-1.9469281993079768e-303	2.270033269815668e-298	-3.4130425136327e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms

analyze1.3s

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

sample4.1s

Algorithm

intervals

Results

1.6s	2060×	body	1280	invalid
894.0ms	7579×	body	80	valid
650.0ms	1246×	body	640	invalid
170.0ms	469×	body	320	invalid
95.0ms	57×	body	2560	invalid
86.0ms	165×	body	640	valid
80.0ms	108×	body	1280	valid
46.0ms	382×	body	80	invalid
44.0ms	106×	body	320	valid
38.0ms	154×	body	160	invalid
10.0ms	42×	body	160	valid

Details

analyze1.5s

sample140.0ms

simplify517.0ms

prune19.0ms

localize24.0ms

rewrite35.0ms

series83.0ms

simplify62.0ms

prune150.0ms

localize29.0ms

rewrite23.0ms

series176.0ms

simplify59.0ms

prune161.0ms

localize38.0ms

rewrite23.0ms

series176.0ms

simplify45.0ms

prune184.0ms

localize45.0ms

rewrite22.0ms

series218.0ms

simplify60.0ms

prune207.0ms

regimes581.0ms

bsearch1.6s

simplify2.0ms

end0.0ms

analyze1.3s

sample4.1s

Profiling