Details

sample376.0ms

Algorithm

intervals

Results

45.0ms	62×	body	1280	valid
30.0ms	253×	body	80	valid
18.0ms	36×	body	640	valid
6.0ms	18×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid

simplify40.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.8b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(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.im)
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)))

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

prune377.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	10	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	10	79

Merged error: 20.0b

Counts

79 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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)
3.0ms	(* (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)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (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)))
153.0ms	(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

prune380.0ms

Filtered

80 candidates to 61 candidates (76.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	10	80
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Merged error: 3.9b

Counts

90 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
32.5b	(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)
4.0ms	(* (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)))

series288.0ms

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)
155.0ms	(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

prune330.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 3.5b

Counts

96 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
0.9b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
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)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`cbrt-prod`
21×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
10×	`add-exp-log`
9×	`swap-sqr`
8×	`add-cbrt-cube`
6×	`pow1/3` `log-pow` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `sin-sum`

Counts

4 → 97

Calls

4 calls:

7.0ms	(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
4.0ms	(* (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))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
16.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
152.0ms	(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)))

simplify116.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	267	826
1	852	743
2	3601	688
3	5002	683

prune365.0ms

Filtered

109 candidates to 73 candidates (67.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	105	16	121

Merged error: 3.4b

Counts

121 → 16

regimes363.0ms

Accuracy

0% (0.7b remaining)

Error of 3.7b against oracle of 3.0b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	26
1	28	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2132×	body	1280	valid
843.0ms	7949×	body	80	valid
708.0ms	1440×	body	640	valid
197.0ms	568×	body	320	valid
71.0ms	43×	body	2560	valid
51.0ms	230×	body	160	valid