Details

sample390.0ms

Algorithm

intervals

Results

43.0ms	60×	body	1280	valid
29.0ms	249×	body	80	valid
21.0ms	43×	body	640	valid
4.0ms	13×	body	320	valid
3.0ms	2×	body	2560	valid
3.0ms	11×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 31.2b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(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

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

series257.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
167.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune304.0ms

Filtered

68 candidates to 54 candidates (79.4%)

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: 17.4b

Counts

70 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(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)))
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 (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
94.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
269.0ms	(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)))

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	226	599
1	690	543
2	2010	539
3	5002	538

prune416.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 17.4b

Counts

70 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.9b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (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)))
13.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
94.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
94.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
266.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	228	623
1	695	563
2	2039	559
3	5001	558

prune441.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 17.4b

Counts

72 → 11

localize39.0ms

Local error

Found 4 expressions with local error:

27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
36.0b	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (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)))
13.0ms	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
95.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
94.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
270.0ms	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	229	647
1	696	583
2	2040	579
3	5002	578

prune403.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	61	11	72

Merged error: 17.4b

Counts

72 → 11

regimes395.0ms

Accuracy

76.8% (3.2b remaining)

Error of 22.4b against oracle of 19.2b and baseline of 33.0b

bsearch145.0ms

Steps

Iters	Range		Point
8	-8.202692737337442e-299	-2.8492448751926983e-303	-2.8912905477472826e-303

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2213×	body	1280	valid
852.0ms	7963×	body	80	valid
689.0ms	1402×	body	640	valid
190.0ms	562×	body	320	valid
85.0ms	53×	body	2560	valid
59.0ms	255×	body	160	valid