Details

sample387.0ms

Algorithm

intervals

Results

51.0ms	73×	body	1280	valid
29.0ms	249×	body	80	valid
21.0ms	44×	body	640	valid
20.0ms	27×	body	320	valid
3.0ms	14×	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: 33.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (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×	`cos-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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2496	381
4	5001	381

prune290.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 19.9b

Counts

70 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
88.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2118	481
3	5001	481

prune243.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 4.5b

Counts

87 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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×	`cos-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)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
131.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
132.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
131.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify158.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (51.0ms)

Iter	Nodes	Cost
0	137	538
1	283	472
2	606	472
3	1518	472
4	4761	471
5	5001	471

prune320.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	49	9	58

Merged error: 4.5b

Counts

58 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (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

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `cos-sum` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
135.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
130.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
133.0ms	(cos (+ (* (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

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	60	584
1	81	500
2	117	500
3	268	500
4	549	500
5	5001	500

prune269.0ms

Filtered

44 candidates to 44 candidates (100.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 4.5b

Counts

53 → 9

regimes428.0ms

Accuracy

79.2% (6.2b remaining)

Error of 9.6b against oracle of 3.4b and baseline of 33.1b

bsearch123.0ms

Steps

Iters	Range		Point
9	-3.207337188926682e-287	-3.8022484328853887e-292	-3.834197278362122e-292

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2003×	body	1280	valid
840.0ms	7995×	body	80	valid
670.0ms	1432×	body	640	valid
219.0ms	668×	body	320	valid
73.0ms	336×	body	160	valid