Details

sample366.0ms

Algorithm

intervals

Results

217.0ms	48×	body	640	valid
71.0ms	90×	body	1280	valid
32.0ms	249×	body	80	valid
10.0ms	27×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	6×	body	160	valid

simplify517.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4996	36
1	4996	36

prune21.0ms

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: 33.5b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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)))
23.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (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)))
66.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify53.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4838	689
1	4838	689

prune156.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

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: 19.5b

Counts

70 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b	(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

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)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4945	851
1	4945	851

prune125.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	51	9	60

Merged error: 19.5b

Counts

60 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b	(* y.re (atan2 x.im x.re))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite18.0ms

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* y.re (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4838	689
1	4838	689

prune147.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	68	9	77

Merged error: 19.5b

Counts

77 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite17.0ms

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)))
3.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4880	761
1	4880	761

prune94.0ms

Filtered

52 candidates to 61 candidates (-17.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

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

Merged error: 19.5b

Counts

70 → 9

regimes471.0ms

Accuracy

81.3% (3.1b remaining)

Error of 22.7b against oracle of 19.5b and baseline of 36.2b

bsearch62.0ms

Steps

Iters	Range		Point
6	-3.294359780484127e-308	3.179664591143469e-308	-6.7692792669888e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	2342×	body	1280	valid
938.0ms	7962×	body	80	valid
752.0ms	1448×	body	640	valid
190.0ms	524×	body	320	valid
84.0ms	48×	body	2560	valid
52.0ms	217×	body	160	valid

Details

sample366.0ms

simplify517.0ms

prune21.0ms

localize26.0ms

rewrite36.0ms

series84.0ms

simplify53.0ms

prune156.0ms

localize30.0ms

rewrite23.0ms

series171.0ms

simplify59.0ms

prune125.0ms

localize24.0ms

rewrite18.0ms

series71.0ms

simplify48.0ms

prune147.0ms

localize32.0ms

rewrite17.0ms

series105.0ms

simplify72.0ms

prune94.0ms

regimes471.0ms

bsearch62.0ms

simplify2.0ms

end0.0ms

sample4.5s

Profiling