Details

sample394.0ms

Algorithm

intervals

Results

59.0ms	77×	body	1280	valid
32.0ms	42×	body	640	valid
27.0ms	249×	body	80	valid
9.0ms	26×	body	320	valid
1.0ms	5×	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

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: 31.9b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
27.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(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)))

series260.0ms

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)))
169.0ms	(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

prune390.0ms

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: 18.5b

Counts

80 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
27.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(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:

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	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms	(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 (19.0ms)

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

prune393.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 4.8b

Counts

90 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
1.1b	(* (atan2 x.im x.re) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
33.7b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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)
3.0ms	(* (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)))

series297.0ms

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)
17.0ms	(* (atan2 x.im x.re) y.im)
161.0ms	(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 (17.0ms)

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

prune345.0ms

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	9	1	10
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Merged error: 4.3b

Counts

94 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
1.0b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
2.7b	(* (atan2 x.im x.re) y.im)
33.6b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt y.re)
7.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt y.re)
88.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
16.0ms	(* (atan2 x.im x.re) y.im)
183.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify103.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	245	484
1	824	412
2	3545	405
3	5002	399

prune300.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	76	13	89

Merged error: 4.3b

Counts

89 → 13

regimes305.0ms

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2269×	body	1280	valid
857.0ms	7936×	body	80	valid
716.0ms	1464×	body	640	valid
192.0ms	571×	body	320	valid
62.0ms	38×	body	2560	valid
55.0ms	248×	body	160	valid