Details

analyze1.5s

Algorithm: search

sample140.0ms

Algorithm

intervals

Results

48.0ms	67×	body	1280	invalid
27.0ms	244×	body	80	valid
27.0ms	48×	body	640	invalid
7.0ms	21×	body	320	invalid
3.0ms	12×	body	160	invalid
2.0ms	5×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	9×	body	80	invalid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify406.0ms

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

prune20.0ms

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: 32.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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)))

series90.0ms

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)))
72.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune120.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 18.1b

Counts

70 → 5

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)
1.5b	(* (atan2 x.im x.re) y.im)
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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)))
8.0ms	(* (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:

38.0ms	(exp (- (* (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)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (52.0ms)

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

prune132.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 3.1b

Counts

86 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b	(cbrt (* (atan2 x.im x.re) y.im))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (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

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (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)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (* (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)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	198	417
1	398	382
2	837	376
3	2125	374
4	5002	372

prune111.0ms

Filtered

50 candidates to 59 candidates (-18.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	60	7	67

Merged error: 3.1b

Counts

67 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

6.4b	(cbrt (* (atan2 x.im x.re) y.im))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (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)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (* (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)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	198	417
1	398	382
2	837	376
3	2125	374
4	5002	372

prune94.0ms

Filtered

50 candidates to 59 candidates (-18.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	59	7	66

Merged error: 3.1b

Counts

66 → 7

regimes401.0ms

Accuracy

64.4% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 19.7b

bsearch2.7s

Steps

Iters	Range		Point
10	-2.001739175301218e-304	1.6231234508257573e-295	2.9550669065017565e-308
8	-6.172024784774524e-10	-3.638431766424105e-13	-4.5851827076107066e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	52	26
2	52	26

end0.0ms

analyze1.2s

Algorithm: search

sample3.7s

Algorithm

intervals

Results

1.3s	1890×	body	1280	invalid
818.0ms	7562×	body	80	valid
656.0ms	1385×	body	640	invalid
190.0ms	583×	body	320	invalid
91.0ms	130×	body	1280	valid
69.0ms	148×	body	640	valid
52.0ms	230×	body	160	invalid
47.0ms	423×	body	80	invalid
33.0ms	99×	body	320	valid
14.0ms	61×	body	160	valid

Details

analyze1.5s

sample140.0ms

simplify406.0ms

prune20.0ms

localize24.0ms

rewrite21.0ms

series90.0ms

simplify80.0ms

prune120.0ms

localize16.0ms

rewrite21.0ms

series73.0ms

simplify59.0ms

prune132.0ms

localize27.0ms

rewrite16.0ms

series83.0ms

simplify65.0ms

prune111.0ms

localize31.0ms

rewrite17.0ms

series83.0ms

simplify66.0ms

prune94.0ms

regimes401.0ms

bsearch2.7s

simplify2.0ms

end0.0ms

analyze1.2s

sample3.7s

Profiling