Details

sample383.0ms

Algorithm

intervals

Results

52.0ms	78×	body	1280	valid
25.0ms	262×	body	80	valid
24.0ms	55×	body	640	valid
4.0ms	14×	body	320	valid
3.0ms	2×	body	2560	valid
2.0ms	9×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

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

series269.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
173.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	213	458
1	565	417
2	1299	415
3	2889	415
4	5003	415

prune377.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Merged error: 19.7b

Counts

79 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+` `hypot-def`

Counts

4 → 68

Calls

4 calls:

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify95.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	259	390
1	731	350
2	1732	349
3	3569	349
4	5002	349

prune367.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 3.7b

Counts

87 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
32.8b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
9×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow`

Counts

4 → 71

Calls

4 calls:

4.0ms	(* (log (hypot x.re x.im)) y.im)
4.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (hypot x.re x.im)) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
158.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	223	400
1	696	351
2	1619	349
3	2891	349
4	5001	349

prune327.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 3.4b

Counts

91 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
1.2b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
1.4b	(* (atan2 x.im x.re) y.re)
32.8b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`sin-sum`

Counts

4 → 77

Calls

4 calls:

10.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
7.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
88.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
17.0ms	(* (atan2 x.im x.re) y.re)
160.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify40.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	290	616
1	1191	504
2	5002	473

prune305.0ms

Filtered

89 candidates to 61 candidates (68.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 3.4b

Counts

101 → 12

regimes276.0ms

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2211×	body	1280	valid
708.0ms	7981×	body	80	valid
613.0ms	1458×	body	640	valid
164.0ms	572×	body	320	valid
60.0ms	39×	body	2560	valid
44.0ms	236×	body	160	valid