Details

sample396.0ms

Algorithm

intervals

Results

59.0ms	81×	body	1280	valid
37.0ms	255×	body	80	valid
21.0ms	46×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	12×	body	160	valid

simplify41.0ms

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: 33.9b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(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×	`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×	`cos-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.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	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms	(cos (+ (* (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 (16.0ms)

Iter	Nodes	Cost
0	207	456
1	556	415
2	1286	411
3	2863	411
4	5002	411

prune348.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 18.4b

Counts

79 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(cos (+ (* (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` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`

Counts

4 → 68

Calls

4 calls:

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

series216.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms	(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify93.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	253	386
1	722	346
2	1719	345
3	3543	345
4	5002	345

prune344.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Merged error: 3.3b

Counts

86 → 6

localize22.0ms

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)
1.9b	(* (atan2 x.im x.re) y.im)
33.2b	(cos (+ (* (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×	`cos-sum` `log-pow`

Counts

4 → 71

Calls

4 calls:

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

series282.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (log (hypot x.re x.im)) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
142.0ms	(cos (+ (* (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 (17.0ms)

Iter	Nodes	Cost
0	220	396
1	690	347
2	1609	345
3	2876	345
4	5001	345

prune304.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 3.0b

Counts

89 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
33.0b	(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt (log (hypot x.re x.im)))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (log (hypot x.re x.im)))
16.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
148.0ms	(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	200	498
1	530	436
2	1204	434
3	2104	432
4	5002	432

prune271.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 3.0b

Counts

85 → 10

regimes237.0ms

Accuracy

0% (0.3b remaining)

Error of 3.2b against oracle of 2.9b and baseline of 3.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	26
1	28	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2077×	body	1280	valid
822.0ms	8006×	body	80	valid
673.0ms	1449×	body	640	valid
209.0ms	652×	body	320	valid
70.0ms	320×	body	160	valid

Details

sample396.0ms

simplify41.0ms

prune13.0ms

localize23.0ms

rewrite23.0ms

series250.0ms

simplify82.0ms

prune348.0ms

localize28.0ms

rewrite17.0ms

series216.0ms

simplify93.0ms

prune344.0ms

localize22.0ms

rewrite17.0ms

series282.0ms

simplify75.0ms

prune304.0ms

localize22.0ms

rewrite21.0ms

series330.0ms

simplify62.0ms

prune271.0ms

regimes237.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling