Details

sample327.0ms

Algorithm

intervals

Results

222.0ms	251×	body	80	valid
46.0ms	65×	body	1280	valid
19.0ms	39×	body	640	valid
8.0ms	25×	body	320	valid
2.0ms	9×	body	160	valid

simplify37.0ms

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 (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: 34.3b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(cos (+ (* (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×	`cos-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	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series89.0ms

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)))
70.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	428
1	523	391
2	1179	387
3	2665	387
4	5002	387

prune112.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Merged error: 19.2b

Counts

69 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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:

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

series77.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune122.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	79	6	85

Merged error: 4.0b

Counts

85 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* (atan2 x.im x.re) y.im))
0.2b	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.9b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `add-log-exp`
4×	`sqr-pow`
3×	`div-exp` `associate-r` `associate-l` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

2.0ms	(exp (* (atan2 x.im x.re) y.im))
5.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series45.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(exp (* (atan2 x.im x.re) y.im))
30.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms	(* (atan2 x.im x.re) y.im)

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	599
1	1004	563
2	5001	558

prune104.0ms

Filtered

82 candidates to 58 candidates (29.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	81	7	88

Merged error: 4.0b

Counts

88 → 7

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
0.5b	(exp (atan2 x.im x.re))
0.5b	(pow (exp (atan2 x.im x.re)) y.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

51×	`unpow-prod-down`
49×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`sqr-pow`
12×	`add-exp-log`
9×	`div-exp`
7×	`pow-to-exp` `pow-exp` `associate-/r` `associate-/l`
6×	`exp-prod`
5×	`add-cbrt-cube`
4×	`pow1` `pow-pow` `add-log-exp`
3×	`pow-unpow`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv` `rem-exp-log`

Counts

3 → 114

Calls

3 calls:

6.0ms	(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
2.0ms	(exp (atan2 x.im x.re))
3.0ms	(pow (exp (atan2 x.im x.re)) y.im)

series49.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
4.0ms	(exp (atan2 x.im x.re))
13.0ms	(pow (exp (atan2 x.im x.re)) y.im)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	1045
1	1379	1017
2	5002	1012

prune101.0ms

Filtered

123 candidates to 83 candidates (32.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	123	7	130

Merged error: 4.0b

Counts

130 → 7

regimes568.0ms

Accuracy

73.1% (7.8b remaining)

Error of 11.9b against oracle of 4.1b and baseline of 33.1b

bsearch88.0ms

Steps

Iters	Range		Point
10	-4.315284471027935e-308	4.85155692442344e-291	-4.6138480611084e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	34	14
2	34	14

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	2022×	body	1280	valid
843.0ms	7959×	body	80	valid
694.0ms	1454×	body	640	valid
226.0ms	683×	body	320	valid
71.0ms	311×	body	160	valid

Details

sample327.0ms

simplify37.0ms

prune16.0ms

localize31.0ms

rewrite22.0ms

series89.0ms

simplify81.0ms

prune112.0ms

localize16.0ms

rewrite18.0ms

series77.0ms

simplify60.0ms

prune122.0ms

localize10.0ms

rewrite12.0ms

series45.0ms

simplify35.0ms

prune104.0ms

localize14.0ms

rewrite16.0ms

series49.0ms

simplify46.0ms

prune101.0ms

regimes568.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample3.9s

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