Details

sample389.0ms

Algorithm

intervals

Results

50.0ms	56×	body	1280	valid
30.0ms	262×	body	80	valid
28.0ms	60×	body	640	valid
6.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify38.0ms

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: 33.2b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(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)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2494	381
4	5002	381

prune312.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 18.1b

Counts

70 → 8

localize16.0ms

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)
2.2b	(* (atan2 x.im x.re) y.im)
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2165	481
3	5001	481

prune262.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 3.5b

Counts

89 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
135.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
137.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify163.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	137	538
1	283	472
2	606	472
3	1507	472
4	4743	471
5	5002	471

prune333.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	50	11	61

Merged error: 3.5b

Counts

61 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
137.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify164.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	137	538
1	283	472
2	606	472
3	1507	472
4	4743	471
5	5002	471

prune341.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	51	11	62

Merged error: 3.5b

Counts

62 → 11

regimes477.0ms

Accuracy

82% (5.4b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 33.8b

bsearch81.0ms

Steps

Iters	Range		Point
6	-1.278936478791097e-308	8.023207831786666e-308	-4.59060153768456e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	1975×	body	1280	valid
808.0ms	7958×	body	80	valid
667.0ms	1444×	body	640	valid
217.0ms	653×	body	320	valid
73.0ms	333×	body	160	valid

Details

sample389.0ms

simplify38.0ms

prune16.0ms

localize25.0ms

rewrite23.0ms

series252.0ms

simplify78.0ms

prune312.0ms

localize16.0ms

rewrite19.0ms

series247.0ms

simplify61.0ms

prune262.0ms

localize27.0ms

rewrite24.0ms

series448.0ms

simplify163.0ms

prune333.0ms

localize36.0ms

rewrite25.0ms

series455.0ms

simplify164.0ms

prune341.0ms

regimes477.0ms

bsearch81.0ms

simplify2.0ms

end0.0ms

sample3.5s

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