Details

sample401.0ms

Algorithm

intervals

Results

58.0ms	63×	body	1280	valid
30.0ms	250×	body	80	valid
21.0ms	42×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	2×	body	2560	valid
3.0ms	11×	body	160	valid

simplify42.0ms

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

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: 35.8b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (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×	`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)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

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

prune362.0ms

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: 21.4b

Counts

80 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(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.im)
4.0ms	(* (atan2 x.im x.re) y.re)
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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify92.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (18.0ms)

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

prune358.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 4.3b

Counts

89 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
1.0b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
32.6b	(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)
3.0ms	(* (atan2 x.im x.re) 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)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (log (hypot x.re x.im)) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
148.0ms	(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 (17.0ms)

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

prune319.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 3.7b

Counts

92 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log (hypot x.re x.im)))
1.0b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
32.7b	(sin (+ (* (* (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×	`sin-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.im)
4.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(sin (+ (* (* (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)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (log (hypot x.re x.im)))
16.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
149.0ms	(sin (+ (* (* (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)))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	205	502
1	538	440
2	1216	438
3	2129	436
4	5001	436

prune272.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	72	17	89

Merged error: 3.6b

Counts

89 → 17

regimes368.0ms

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	26	26
1	26	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2169×	body	1280	valid
857.0ms	7928×	body	80	valid
685.0ms	1409×	body	640	valid
187.0ms	557×	body	320	valid
69.0ms	43×	body	2560	valid
55.0ms	243×	body	160	valid