Details

sample369.0ms

Algorithm

intervals

Results

42.0ms	64×	body	1280	valid
27.0ms	256×	body	80	valid
22.0ms	49×	body	640	valid
6.0ms	4×	body	2560	valid
6.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify54.0ms

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: 32.1b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b	(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.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)))

series252.0ms

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)))
34.0ms	(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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

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

prune379.0ms

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: 18.4b

Counts

80 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.im)
0.7b	(* (atan2 x.im x.re) y.re)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b	(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)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (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)))
153.0ms	(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	74	6	80
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 2.7b

Counts

89 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
0.7b	(* (atan2 x.im x.re) y.im)
0.7b	(* (atan2 x.im x.re) y.re)
32.0b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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:

7.0ms	(* (log (hypot x.re x.im)) y.im)
4.0ms	(* (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)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (log (hypot x.re x.im)) y.im)
19.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
150.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

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

prune330.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	77	14	91

Merged error: 2.4b

Counts

91 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (log (hypot x.re x.im)) y.im))
0.8b	(cbrt (* (log (hypot x.re x.im)) y.im))
0.8b	(cbrt (* (log (hypot x.re x.im)) y.im))
32.1b	(sin (+ (* (* (cbrt (* (log (hypot x.re x.im)) y.im)) (cbrt (* (log (hypot x.re x.im)) y.im))) (cbrt (* (log (hypot x.re x.im)) y.im))) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

2.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
3.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
3.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
11.0ms	(sin (+ (* (* (cbrt (* (log (hypot x.re x.im)) y.im)) (cbrt (* (log (hypot x.re x.im)) y.im))) (cbrt (* (log (hypot x.re x.im)) y.im))) (* (atan2 x.im x.re) y.re)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
162.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
158.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
178.0ms	(sin (+ (* (* (cbrt (* (log (hypot x.re x.im)) y.im)) (cbrt (* (log (hypot x.re x.im)) y.im))) (cbrt (* (log (hypot x.re x.im)) y.im))) (* (atan2 x.im x.re) y.re)))

simplify50.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	132	554
1	220	490
2	509	475
3	1437	463
4	5002	460

prune252.0ms

Filtered

55 candidates to 51 candidates (92.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	54	15	69

Merged error: 2.4b

Counts

69 → 15

regimes330.0ms

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	28	28
1	28	28

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2090×	body	1280	valid
724.0ms	7989×	body	80	valid
604.0ms	1381×	body	640	valid
159.0ms	543×	body	320	valid
66.0ms	42×	body	2560	valid
49.0ms	253×	body	160	valid