Details

sample381.0ms

Algorithm

intervals

Results

43.0ms	60×	body	1280	valid
28.0ms	249×	body	80	valid
21.0ms	43×	body	640	valid
4.0ms	13×	body	320	valid
3.0ms	2×	body	2560	valid
2.0ms	11×	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

prune21.0ms

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: 31.2b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(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.im)
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)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
167.0ms	(sin (+ (* (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 (15.0ms)

Iter	Nodes	Cost
0	213	458
1	565	417
2	1299	415
3	2889	415
4	5003	415

prune374.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	9	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 17.4b

Counts

80 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
2.5b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(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.re)
4.0ms	(* (atan2 x.im x.re) y.im)
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)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify96.0ms

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

prune381.0ms

Filtered

80 candidates to 61 candidates (76.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	78	12	90

Merged error: 4.1b

Counts

90 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
1.7b	(* (atan2 x.im x.re) y.re)
2.5b	(* (atan2 x.im x.re) y.im)
35.8b	(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.re)
4.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (log (hypot x.re x.im)) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
158.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

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

prune338.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 3.7b

Counts

95 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (log (hypot x.re x.im)) y.im))
1.7b	(* (atan2 x.im x.re) y.re)
2.5b	(* (atan2 x.im x.re) y.im)
36.1b	(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)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
3.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(* (atan2 x.im x.re) 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)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (* (log (hypot x.re x.im)) y.im))
16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
183.0ms	(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)))

simplify89.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (83.0ms)

Iter	Nodes	Cost
0	231	534
1	603	468
2	1481	463
3	3270	459
4	5002	457

prune265.0ms

Filtered

73 candidates to 55 candidates (75.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	69	18	87

Merged error: 3.6b

Counts

87 → 18

regimes400.0ms

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	24
1	26	24

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2213×	body	1280	valid
848.0ms	7963×	body	80	valid
684.0ms	1402×	body	640	valid
189.0ms	562×	body	320	valid
84.0ms	53×	body	2560	valid
56.0ms	255×	body	160	valid