Details

sample371.0ms

Algorithm

intervals

Results

48.0ms	78×	body	1280	valid
24.0ms	256×	body	80	valid
17.0ms	42×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

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

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: 33.7b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (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

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:

4.0ms	(* (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)))
10.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	211	458
1	555	417
2	1277	415
3	2762	415
4	5002	415

prune408.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 19.5b

Counts

80 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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:

4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify114.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	263	404
1	755	360
2	1828	359
3	4355	359
4	5001	359

prune409.0ms

Filtered

80 candidates to 61 candidates (76.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 3.4b

Counts

89 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
5.7b	(exp (log (hypot x.re x.im)))
34.4b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.re)
2.0ms	(exp (log (hypot x.re x.im)))
7.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
49.0ms	(exp (log (hypot x.re x.im)))
150.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	208	362
1	566	317
2	1248	317
3	2201	313
4	5001	313

prune410.0ms

Filtered

79 candidates to 58 candidates (73.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	76	12	88

Merged error: 3.4b

Counts

88 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
5.7b	(exp (log (hypot x.re x.im)))
34.4b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`pow1/3`
1×	`sin-sum` `log-pow` `rem-exp-log`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(exp (log (hypot x.re x.im)))
7.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt (atan2 x.im x.re))
39.0ms	(cbrt (atan2 x.im x.re))
49.0ms	(exp (log (hypot x.re x.im)))
154.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify55.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	128	322
1	231	287
2	405	283
3	1082	277
4	5001	277

prune359.0ms

Filtered

65 candidates to 53 candidates (81.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	64	13	77

Merged error: 3.4b

Counts

77 → 13

regimes367.0ms

Accuracy

0% (0.1b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 3.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	33
1	40	33
2	40	33

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2246×	body	1280	valid
685.0ms	7980×	body	80	valid
564.0ms	1367×	body	640	valid
153.0ms	546×	body	320	valid
58.0ms	39×	body	2560	valid
39.0ms	215×	body	160	valid