Details

sample399.0ms

Algorithm

intervals

Results

69.0ms	77×	body	1280	valid
26.0ms	249×	body	80	valid
21.0ms	42×	body	640	valid
9.0ms	26×	body	320	valid
1.0ms	5×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune16.0ms

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

localize24.0ms

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)))

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×	`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:

4.0ms	(* (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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune321.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 18.5b

Counts

70 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

27.4b	(sqrt (+ (* x.re x.re) (* x.im x.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 (* (* (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)))

rewrite40.0ms

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)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(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)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	148	607
1	303	551
2	643	551
3	1821	551
4	5001	548

prune356.0ms

Filtered

65 candidates to 55 candidates (84.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	65	11	76

Merged error: 18.5b

Counts

76 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (atan2 x.im x.re))
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)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (atan2 x.im x.re))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	160	405
1	334	373
2	731	371
3	1992	371
4	5002	369

prune322.0ms

Filtered

61 candidates to 51 candidates (83.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	61	11	72

Merged error: 18.5b

Counts

72 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (atan2 x.im x.re))
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)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (atan2 x.im x.re))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	160	405
1	334	373
2	731	371
3	1992	371
4	5002	369

prune305.0ms

Filtered

61 candidates to 51 candidates (83.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	62	10	72

Merged error: 18.5b

Counts

72 → 10

regimes319.0ms

Accuracy

66.2% (4.6b remaining)

Error of 23.8b against oracle of 19.1b and baseline of 32.9b

bsearch275.0ms

Steps

Iters	Range		Point
8	4.7581553547983534e-189	4.705645763359602e-185	8.479128448291586e-189
10	-6.2720510697352396e-46	-1.4633507478050622e-62	-5.849570790092907e-48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	69
1	54	69

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2269×	body	1280	valid
844.0ms	7936×	body	80	valid
713.0ms	1464×	body	640	valid
192.0ms	571×	body	320	valid
62.0ms	38×	body	2560	valid
55.0ms	248×	body	160	valid