Details

sample365.0ms

Algorithm

intervals

Results

66.0ms	86×	body	1280	valid
31.0ms	254×	body	80	valid
20.0ms	40×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify530.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune20.0ms

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: 27.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(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.im)
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.im)
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)))

simplify49.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5069	689

prune152.0ms

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: 14.0b

Counts

70 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(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)))

rewrite25.0ms

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)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(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)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(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)))
129.0ms	(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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4881	889
1	4881	889

prune140.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

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: 14.0b

Counts

70 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(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)))
55.0ms	(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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5054	851

prune125.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	50	10	60

Merged error: 14.0b

Counts

60 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(* y.re (atan2 x.im x.re))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(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))
4.0ms	(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))))

series72.0ms

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

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5128	689

prune96.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	68	10	78

Merged error: 14.0b

Counts

78 → 10

regimes454.0ms

Accuracy

74.9% (3.5b remaining)

Error of 22.3b against oracle of 18.8b and baseline of 32.8b

bsearch213.0ms

Steps

Iters	Range	Point
6	5.3773262060695594e-61	6.875234800690788e-60	1.1812805417144586e-60
6	1.4126018779062698e-247	1.1264860254360087e-246	1.1131057807197489e-246
9	-2.9885431692775155e-304	2.648985686240207e-304	-1.7600018223762e-310

Iters

Range

Point

5.3773262060695594e-61

6.875234800690788e-60

1.1812805417144586e-60

1.4126018779062698e-247

1.1264860254360087e-246

1.1131057807197489e-246

-2.9885431692775155e-304

2.648985686240207e-304

-1.7600018223762e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	122
1	92	122

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	2209×	body	1280	valid
885.0ms	7971×	body	80	valid
701.0ms	1403×	body	640	valid
194.0ms	562×	body	320	valid
85.0ms	49×	body	2560	valid
60.0ms	255×	body	160	valid

Details

sample365.0ms

simplify530.0ms

prune20.0ms

localize24.0ms

rewrite36.0ms

series84.0ms

simplify49.0ms

prune152.0ms

localize30.0ms

rewrite25.0ms

series179.0ms

simplify53.0ms

prune140.0ms

localize28.0ms

rewrite27.0ms

series171.0ms

simplify44.0ms

prune125.0ms

localize25.0ms

rewrite18.0ms

series72.0ms

simplify45.0ms

prune96.0ms

regimes454.0ms

bsearch213.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling