Details

sample351.0ms

Algorithm

intervals

Results

249.0ms	76×	body	1280	valid
33.0ms	253×	body	80	valid
24.0ms	44×	body	640	valid
7.0ms	20×	body	320	valid
4.0ms	15×	body	160	valid

simplify503.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

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: 27.8b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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)))
24.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series82.0ms

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)))
63.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify47.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	677

prune112.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 14.0b

Counts

70 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.8b	(* (atan2 x.im x.re) y.im)
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4931	898
1	4931	898

prune106.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 2.8b

Counts

81 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* y.re (atan2 x.im x.re))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite19.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* y.re (atan2 x.im x.re))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

simplify42.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5098	677

prune98.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	68	5	73

Merged error: 2.8b

Counts

73 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log x.re) y.re)
1.8b	(* (atan2 x.im x.re) y.im)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

4.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
6.0ms	(* (log x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series60.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
21.0ms	(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
10.0ms	(* (log x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5191	643

prune70.0ms

Filtered

49 candidates to 76 candidates (-55.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	76	5	81

Merged error: 2.8b

Counts

81 → 5

regimes286.0ms

Accuracy

61.6% (6.1b remaining)

Error of 9.3b against oracle of 3.3b and baseline of 19.0b

bsearch229.0ms

Steps

Iters	Range	Point
9	1.2815190686638593e+141	6.093512154029396e+149	1.3029601913589053e+141
9	1.8702125469004368e-152	7.7176146432404825e-146	3.752270320775175e-151
9	-2.9885431692775155e-304	2.648985686240207e-304	-1.7600018223762e-310

Iters

Range

Point

1.2815190686638593e+141

6.093512154029396e+149

1.3029601913589053e+141

1.8702125469004368e-152

7.7176146432404825e-146

3.752270320775175e-151

-2.9885431692775155e-304

2.648985686240207e-304

-1.7600018223762e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	54
1	82	54

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2037×	body	1280	valid
844.0ms	7993×	body	80	valid
662.0ms	1427×	body	640	valid
215.0ms	649×	body	320	valid
74.0ms	343×	body	160	valid

Details

sample351.0ms

simplify503.0ms

prune19.0ms

localize23.0ms

rewrite38.0ms

series82.0ms

simplify47.0ms

prune112.0ms

localize18.0ms

rewrite18.0ms

series73.0ms

simplify48.0ms

prune106.0ms

localize26.0ms

rewrite19.0ms

series69.0ms

simplify42.0ms

prune98.0ms

localize10.0ms

rewrite19.0ms

series60.0ms

simplify44.0ms

prune70.0ms

regimes286.0ms

bsearch229.0ms

simplify2.0ms

end0.0ms

sample3.8s

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