Details

sample362.0ms

Algorithm

intervals

Results

70.0ms	90×	body	1280	valid
31.0ms	249×	body	80	valid
24.0ms	48×	body	640	valid
10.0ms	27×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	6×	body	160	valid

simplify504.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4996	36
1	4996	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: 33.5b

Counts

2 → 2

localize25.0ms

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)))
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4838	689
1	4838	689

prune154.0ms

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

localize29.0ms

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)))

series166.0ms

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)))
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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4945	851
1	4945	851

prune124.0ms

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))))

rewrite17.0ms

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))))

series70.0ms

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)))
55.0ms	(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 (42.0ms)

Iter	Nodes	Cost
0	4838	689
1	4838	689

prune145.0ms

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

localize31.0ms

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))))

series102.0ms

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)))
21.0ms	(cbrt (+ (* 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))))

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4880	761
1	4880	761

prune95.0ms

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

regimes458.0ms

Accuracy

81.3% (3.1b remaining)

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

bsearch61.0ms

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

sample4.4s

Algorithm

intervals

Results

1.8s	2342×	body	1280	valid
903.0ms	7962×	body	80	valid
746.0ms	1448×	body	640	valid
184.0ms	524×	body	320	valid
81.0ms	48×	body	2560	valid
50.0ms	217×	body	160	valid

Details

sample362.0ms

simplify504.0ms

prune19.0ms

localize25.0ms

rewrite36.0ms

series82.0ms

simplify52.0ms

prune154.0ms

localize29.0ms

rewrite23.0ms

series166.0ms

simplify60.0ms

prune124.0ms

localize24.0ms

rewrite17.0ms

series70.0ms

simplify48.0ms

prune145.0ms

localize31.0ms

rewrite17.0ms

series102.0ms

simplify72.0ms

prune95.0ms

regimes458.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample4.4s

Profiling