Details

sample380.0ms

Algorithm

intervals

Results

52.0ms	80×	body	1280	valid
24.0ms	258×	body	80	valid
21.0ms	51×	body	640	valid
6.0ms	21×	body	320	valid
1.0ms	1×	body	2560	valid
1.0ms	7×	body	160	valid

simplify43.0ms

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

prune16.0ms

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: 32.1b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
52×	`hypot-def`
32×	`*-un-lft-identity`
24×	`swap-sqr`
21×	`*-commutative` `unswap-sqr`
16×	`sqrt-prod`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
169.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	210	490
1	537	451
2	1234	447
3	3100	447
4	5002	447

prune409.0ms

Filtered

139 candidates to 85 candidates (61.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	133	8	141

Merged error: 18.6b

Counts

141 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify96.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	257	413
1	699	372
2	1662	370
3	3909	370
4	5001	370

prune379.0ms

Filtered

111 candidates to 72 candidates (64.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 2.7b

Counts

119 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.im x.re)) y.im)
0.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
30.4b	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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`
2×	`sin-sum`
1×	`+-commutative` `log-pow`

Counts

4 → 72

Calls

4 calls:

4.0ms	(* (log (hypot x.im x.re)) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (hypot x.im x.re)) y.im)
17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
161.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	224	416
1	695	367
2	1606	365
3	2854	365
4	5001	365

prune361.0ms

Filtered

84 candidates to 62 candidates (73.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	15	84
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 2.4b

Counts

95 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log (hypot x.im x.re)))
0.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
30.3b	(sin (+ (* (* (cbrt (log (hypot x.im x.re))) (cbrt (log (hypot x.im x.re)))) (* (cbrt (log (hypot x.im x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite79.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `pow1/3` `log-pow`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (log (hypot x.im x.re)))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
69.0ms	(sin (+ (* (* (cbrt (log (hypot x.im x.re))) (cbrt (log (hypot x.im x.re)))) (* (cbrt (log (hypot x.im x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (log (hypot x.im x.re)))
17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
160.0ms	(sin (+ (* (* (cbrt (log (hypot x.im x.re))) (cbrt (log (hypot x.im x.re)))) (* (cbrt (log (hypot x.im x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	205	536
1	538	474
2	1209	472
3	2124	470
4	5001	470

prune302.0ms

Filtered

77 candidates to 58 candidates (75.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	76	17	93

Merged error: 2.3b

Counts

93 → 17

regimes430.0ms

Accuracy

0% (0.7b remaining)

Error of 3.8b against oracle of 3.1b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	36
1	39	36
2	39	36

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2244×	body	1280	valid
696.0ms	7932×	body	80	valid
591.0ms	1447×	body	640	valid
162.0ms	578×	body	320	valid
65.0ms	44×	body	2560	valid
44.0ms	241×	body	160	valid