Details

sample365.0ms

Algorithm

intervals

Results

227.0ms	55×	body	640	valid
59.0ms	79×	body	1280	valid
28.0ms	252×	body	80	valid
9.0ms	25×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	7×	body	160	valid

simplify292.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.0b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(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×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune170.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	11	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 18.3b

Counts

70 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

Calls

4 calls:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify69.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	156	544
1	346	498
2	780	497
3	2120	497
4	5002	494

prune160.0ms

Filtered

65 candidates to 56 candidates (13.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 18.1b

Counts

77 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	158	616
1	336	558
2	704	557
3	2021	557
4	5001	554

prune161.0ms

Filtered

65 candidates to 56 candidates (13.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	65	12	77

Merged error: 18.1b

Counts

77 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
23.0b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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×	`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-+`

Counts

4 → 59

Calls

4 calls:

5.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	260	372
1	715	332
2	1646	328
3	3711	328
4	5001	328

prune113.0ms

Filtered

71 candidates to 51 candidates (28.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	69	14	83

Merged error: 10.3b

Counts

83 → 14

regimes618.0ms

Accuracy

68.5% (6.3b remaining)

Error of 16.2b against oracle of 9.9b and baseline of 29.8b

bsearch245.0ms

Steps

Iters	Range	Point
10	-3.5765641277586868e-301	3.3873642478406533e-299	-5.00355780878745e-310
8	-5.7450044827993056e-201	-6.915710465369219e-205	-1.8053417554947053e-201
4	-4.52027450578379e-179	-2.4777443684130177e-179	-2.5191425433550405e-179

Iters

Range

Point

-3.5765641277586868e-301

3.3873642478406533e-299

-5.00355780878745e-310

-5.7450044827993056e-201

-6.915710465369219e-205

-1.8053417554947053e-201

-4.52027450578379e-179

-2.4777443684130177e-179

-2.5191425433550405e-179

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	70
1	62	70

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2220×	body	1280	valid
887.0ms	8042×	body	80	valid
699.0ms	1403×	body	640	valid
192.0ms	556×	body	320	valid
75.0ms	45×	body	2560	valid
53.0ms	218×	body	160	valid

Details

sample365.0ms

simplify292.0ms

prune19.0ms

localize35.0ms

rewrite22.0ms

series91.0ms

simplify83.0ms

prune170.0ms

localize27.0ms

rewrite28.0ms

series73.0ms

simplify69.0ms

prune160.0ms

localize29.0ms

rewrite36.0ms

series72.0ms

simplify71.0ms

prune161.0ms

localize24.0ms

rewrite19.0ms

series56.0ms

simplify102.0ms

prune113.0ms

regimes618.0ms

bsearch245.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling