Details

sample358.0ms

Algorithm

intervals

Results

37.0ms	63×	body	1280	valid
23.0ms	251×	body	80	valid
17.0ms	46×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	9×	body	160	valid

simplify42.0ms

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

prune29.0ms

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: 32.5b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (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)))
33.5b	(cos (+ (* (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×	`cos-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	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune300.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 17.4b

Counts

70 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.4b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2118	481
3	5001	481

prune269.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 4.3b

Counts

88 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (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)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `associate-l` `flip-+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 63

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

series122.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	145	374
1	428	355
2	1017	352
3	2145	352
4	5002	352

prune374.0ms

Filtered

75 candidates to 58 candidates (77.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 4.3b

Counts

85 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.4b	(* (atan2 x.im x.re) y.im)
4.0b	(log (exp (* (atan2 x.im x.re) y.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `log-pow`
5×	`add-log-exp`
3×	`log-prod` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `flip3-+` `rem-log-exp` `flip-+`

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	247	426
1	716	377
2	1692	374
3	3958	374
4	5001	374

prune247.0ms

Filtered

80 candidates to 57 candidates (71.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	79	11	90

Merged error: 4.3b

Counts

90 → 11

regimes292.0ms

Accuracy

59.2% (6.5b remaining)

Error of 10.3b against oracle of 3.7b and baseline of 19.8b

bsearch226.0ms

Steps

Iters	Range		Point
9	3.2398009343753024e-119	4.271661016463332e-114	2.597653207771217e-116
10	-2.2735744027913026e-19	-3.3775070190963855e-31	-1.836315703687079e-22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	51
1	56	51
2	56	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2053×	body	1280	valid
658.0ms	7978×	body	80	valid
586.0ms	1482×	body	640	valid
173.0ms	636×	body	320	valid
57.0ms	314×	body	160	valid