Details

sample402.0ms

Algorithm

intervals

Results

69.0ms	86×	body	1280	valid
28.0ms	64×	body	640	valid
24.0ms	248×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	10×	body	160	valid

simplify39.0ms

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: 33.0b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
52×	`hypot-def`
32×	`*-un-lft-identity`
24×	`swap-sqr`
21×	`*-commutative` `unswap-sqr`
16×	`sqrt-prod`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (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)))
166.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify92.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	216	488
1	568	447
2	1321	447
3	3375	447
4	5001	447

prune537.0ms

Filtered

139 candidates to 85 candidates (61.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Merged error: 19.9b

Counts

141 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
26×	`hypot-def`
21×	`*-un-lft-identity`
12×	`swap-sqr` `*-commutative` `unswap-sqr`
10×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
6×	`associate-r`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`+-commutative` `sin-sum` `sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 99

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify122.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	266	426
1	749	382
2	1838	382
3	4962	382
4	5001	382

prune498.0ms

Filtered

111 candidates to 72 candidates (64.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Merged error: 4.4b

Counts

118 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (* 1 (hypot x.re x.im))) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
30.7b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (log (* 1 (hypot x.re x.im))) y.im)
4.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (log (* 1 (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 (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	227	461
1	694	405
2	2006	398
3	5001	396

prune482.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	16	85
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	76	16	92

Merged error: 4.0b

Counts

92 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(log1p (sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
1.4b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
30.7b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `log1p-udef` `log1p-expm1`

Counts

4 → 62

Calls

4 calls:

1.0ms	(log1p (sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
4.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(log1p (sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
16.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
160.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	212	478
1	654	419
2	2338	419
3	5001	418

prune376.0ms

Filtered

74 candidates to 54 candidates (73.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	74	16	90

Merged error: 4.0b

Counts

90 → 16

regimes455.0ms

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	23
1	37	23
2	37	23

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2171×	body	1280	valid
736.0ms	7944×	body	80	valid
601.0ms	1391×	body	640	valid
160.0ms	542×	body	320	valid
80.0ms	48×	body	2560	valid
46.0ms	238×	body	160	valid