Details

sample384.0ms

Algorithm

intervals

Results

37.0ms	61×	body	1280	valid
24.0ms	259×	body	80	valid
14.0ms	36×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid

simplify39.0ms

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

prune28.0ms

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: 33.6b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(cos (+ (* (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

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)))
10.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms	(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

prune298.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 18.5b

Counts

70 → 3

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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.1b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:

5.0ms	(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)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(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)))

simplify59.0ms

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

prune272.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Merged error: 2.6b

Counts

84 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `associate-l` `flip-+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 63

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)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	145	374
1	428	355
2	1017	352
3	2145	352
4	5002	352

prune366.0ms

Filtered

75 candidates to 58 candidates (77.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Merged error: 2.6b

Counts

81 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.1b	(* (log (* -1 x.re)) y.re)
1.1b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`exp-prod` `pow-prod-down`
2×	`exp-sum` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `exp-diff` `diff-log`

Counts

3 → 53

Calls

3 calls:

5.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (* -1 x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series146.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
65.0ms	(* (log (* -1 x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify61.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	214	325
1	697	283
2	2959	278
3	5001	278

prune150.0ms

Filtered

62 candidates to 41 candidates (66.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	61	7	68

Merged error: 2.6b

Counts

68 → 7

regimes247.0ms

Accuracy

63.4% (5.8b remaining)

Error of 9.4b against oracle of 3.6b and baseline of 19.6b

bsearch399.0ms

Steps

Iters	Range		Point
8	1.0396897626580026e-14	1.8250189704727073e-11	1.309115862754305e-12
7	-2.366385312335927e-299	-3.6062401743320616e-301	-3.2093552099949914e-300
9	-9.867827724405996e-246	-2.9078429832612246e-251	-3.0524264572824694e-246
8	-1.989278530209094e-41	-1.2878477493320859e-44	-2.727557833043315e-42

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	119
1	78	119
2	78	119

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2040×	body	1280	valid
677.0ms	7963×	body	80	valid
560.0ms	1442×	body	640	valid
186.0ms	683×	body	320	valid
55.0ms	293×	body	160	valid