Details

sample379.0ms

Algorithm

intervals

Results

42.0ms	68×	body	1280	valid
26.0ms	255×	body	80	valid
22.0ms	54×	body	640	valid
5.0ms	3×	body	2560	valid
5.0ms	16×	body	320	valid
1.0ms	8×	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

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 35.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
155.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	210	488
1	537	451
2	1234	447
3	3100	447
4	5002	447

prune408.0ms

Filtered

139 candidates to 85 candidates (38.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	7	140

Merged error: 19.7b

Counts

140 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite46.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
15.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
165.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	257	413
1	699	372
2	1656	370
3	3903	370
4	5001	370

prune380.0ms

Filtered

111 candidates to 72 candidates (35.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 3.2b

Counts

118 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.im x.re)) y.im)
1.6b	(* (atan2 x.im x.re) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

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`
2×	`sin-sum`
1×	`+-commutative` `log-pow`

Counts

4 → 72

Calls

4 calls:

4.0ms	(* (log (hypot x.im x.re)) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (log (hypot x.im x.re)) y.im)
17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
163.0ms	(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	224	416
1	695	367
2	1606	365
3	2854	365
4	5001	365

prune339.0ms

Filtered

84 candidates to 62 candidates (26.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	13	84
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 2.8b

Counts

93 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

17.3b	(sin (* (atan2 x.im x.re) y.re))
17.6b	(cos (* (atan2 x.im x.re) y.re))
22.2b	(cos (* (log (hypot x.im x.re)) y.im))
22.2b	(sin (* (log (hypot x.im x.re)) y.im))

rewrite19.0ms

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`

Counts

4 → 36

Calls

4 calls:

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

series353.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sin (* (atan2 x.im x.re) y.re))
41.0ms	(cos (* (atan2 x.im x.re) y.re))
136.0ms	(cos (* (log (hypot x.im x.re)) y.im))
134.0ms	(sin (* (log (hypot x.im x.re)) y.im))

simplify103.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	90	252
1	127	218
2	201	215
3	510	215
4	1869	215
5	5001	215

prune257.0ms

Filtered

48 candidates to 44 candidates (8.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	48	13	61

Merged error: 2.8b

Counts

61 → 13

regimes347.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	27
1	33	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2264×	body	1280	valid
693.0ms	7949×	body	80	valid
619.0ms	1491×	body	640	valid
160.0ms	561×	body	320	valid
78.0ms	51×	body	2560	valid
43.0ms	233×	body	160	valid