Details

analyze1.8s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample137.0ms

Algorithm

intervals

Results

44.0ms	69×	body	1280	invalid
30.0ms	242×	body	80	valid
23.0ms	49×	body	640	invalid
5.0ms	15×	body	320	invalid
2.0ms	9×	body	160	invalid
2.0ms	5×	body	320	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	7×	body	80	invalid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4937	72
1	4937	72

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: 35.4b

Counts

2 → 2

localize40.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(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)))

rewrite43.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
95.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5168	1251

prune194.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

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: 21.2b

Counts

70 → 5

localize16.0ms

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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 → 65

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)
5.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
40.0ms	(* (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)))

simplify111.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4934	1660
1	4934	1660

prune224.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 3.6b

Counts

82 → 8

localize42.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (pow x.re 2) (pow x.im 2)))
33.5b	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

16.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
10.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
83.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
67.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
100.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify122.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4938	1552
1	4938	1552

prune460.0ms

Filtered

48 candidates to 53 candidates (-10.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	52	9	61

Merged error: 3.6b

Counts

61 → 9

localize74.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (pow x.re 2) (pow x.im 2)))
31.6b	(sqrt (+ (pow x.re 2) (pow x.im 2)))
33.5b	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `unpow-prod-down` `sqrt-div` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 50

Calls

4 calls:

8.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
8.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
9.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
6.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
72.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
79.0ms	(cos (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify139.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4938	1460
1	4938	1460

prune316.0ms

Filtered

52 candidates to 62 candidates (-19.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	62	9	71

Merged error: 3.6b

Counts

71 → 9

regimes746.0ms

Accuracy

64.7% (5.7b remaining)

Error of 9.1b against oracle of 3.5b and baseline of 19.5b

bsearch163.0ms

Steps

Iters	Range		Point
9	1.2943075703496584e-269	9.742023499667162e-261	1.4537597835968884e-266
7	-2.8961308557603527e-238	-8.322508166596883e-240	-8.419082579799947e-240

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	79	96
1	79	96

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.8s	1888×	body	1280	invalid
1.2s	7554×	body	80	valid
867.0ms	1288×	body	640	invalid
278.0ms	559×	body	320	invalid
113.0ms	160×	body	640	valid
89.0ms	96×	body	1280	valid
81.0ms	256×	body	160	invalid
66.0ms	127×	body	320	valid
61.0ms	372×	body	80	invalid
20.0ms	63×	body	160	valid

Details

analyze1.8s

sample137.0ms

simplify108.0ms

prune19.0ms

localize40.0ms

rewrite43.0ms

series118.0ms

simplify76.0ms

prune194.0ms

localize16.0ms

rewrite20.0ms

series102.0ms

simplify111.0ms

prune224.0ms

localize42.0ms

rewrite41.0ms

series261.0ms

simplify122.0ms

prune460.0ms

localize74.0ms

rewrite40.0ms

series167.0ms

simplify139.0ms

prune316.0ms

regimes746.0ms

bsearch163.0ms

simplify7.0ms

end0.0ms

sample5.1s

Profiling