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

sample142.0ms

Algorithm

intervals

Results

47.0ms	61×	body	1280	invalid
27.0ms	237×	body	80	valid
24.0ms	41×	body	640	invalid
6.0ms	18×	body	320	invalid
4.0ms	6×	body	1280	valid
4.0ms	7×	body	640	valid
3.0ms	11×	body	160	invalid
2.0ms	16×	body	80	invalid
2.0ms	1×	body	2560	invalid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify483.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

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: 34.9b

Counts

2 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series87.0ms

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)))
69.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4750	692
1	4750	692

prune161.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 20.7b

Counts

70 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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)))

rewrite21.0ms

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)))
10.0ms	(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:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
127.0ms	(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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4911	911
1	4911	911

prune167.0ms

Filtered

54 candidates to 61 candidates (-13.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	59	12	71

Merged error: 20.6b

Counts

71 → 12

localize37.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

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

series174.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
126.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

simplify46.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5012	910

prune183.0ms

Filtered

54 candidates to 66 candidates (-22.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	66	12	78

Merged error: 20.6b

Counts

78 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify48.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5038	851

prune84.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	50	13	63

Merged error: 20.6b

Counts

63 → 13

regimes566.0ms

Accuracy

75.4% (3.4b remaining)

Error of 23.3b against oracle of 20.0b and baseline of 33.7b

bsearch1.4s

Steps

Iters	Range		Point
9	-5.062770195702041e-302	-2.3335637489488046e-307	-2.3644610081048188e-307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms

analyze1.2s

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

sample3.9s

Algorithm

intervals

Results

1.5s	2100×	body	1280	invalid
836.0ms	7513×	body	80	valid
619.0ms	1250×	body	640	invalid
175.0ms	508×	body	320	invalid
107.0ms	147×	body	1280	valid
79.0ms	161×	body	640	valid
75.0ms	42×	body	2560	invalid
46.0ms	124×	body	320	valid
42.0ms	190×	body	160	invalid
40.0ms	351×	body	80	invalid
13.0ms	55×	body	160	valid

Details

analyze1.5s

sample142.0ms

simplify483.0ms

prune19.0ms

localize33.0ms

rewrite20.0ms

series87.0ms

simplify57.0ms

prune161.0ms

localize30.0ms

rewrite21.0ms

series176.0ms

simplify60.0ms

prune167.0ms

localize37.0ms

rewrite23.0ms

series174.0ms

simplify46.0ms

prune183.0ms

localize31.0ms

rewrite22.0ms

series167.0ms

simplify48.0ms

prune84.0ms

regimes566.0ms

bsearch1.4s

simplify2.0ms

end0.0ms

analyze1.2s

sample3.9s

Profiling