Details

analyze1.5s

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

sample138.0ms

Algorithm

intervals

Results

42.0ms	56×	body	1280	invalid
28.0ms	241×	body	80	valid
27.0ms	51×	body	640	invalid
10.0ms	18×	body	320	invalid
3.0ms	5×	body	640	valid
2.0ms	8×	body	160	invalid
2.0ms	14×	body	80	invalid
2.0ms	2×	body	1280	valid
1.0ms	5×	body	160	valid
1.0ms	3×	body	320	valid

simplify467.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune28.0ms

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: 34.6b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(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:

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)))

series85.0ms

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)))
67.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify46.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5029	677

prune121.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	1	1
Picked	0	1	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)
1.1b	(* (atan2 x.im x.re) y.im)
31.1b	(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 → 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)
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:

36.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
24.0ms	(* (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)))

simplify49.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4931	892
1	4931	892

prune118.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

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

Merged error: 3.4b

Counts

82 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.0b	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (neg x.re)) y.re)
1.1b	(* (atan2 x.im x.re) y.im)

rewrite17.0ms

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` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`flip3--` `exp-diff` `exp-sum` `log-pow` `flip--`

Counts

4 → 62

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
12.0ms	(* (log (neg x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4979	693
1	4979	693

prune97.0ms

Filtered

52 candidates to 74 candidates (-42.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	74	8	82

Merged error: 3.4b

Counts

82 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(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)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
51.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4993	815
1	4993	815

prune83.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	50	9	59

Merged error: 3.4b

Counts

59 → 9

regimes541.0ms

Accuracy

66.6% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 20.1b

bsearch262.0ms

Steps

Iters	Range		Point
8	4.422363573017874e-48	1.7563168809935758e-45	1.7772110677640783e-47
10	2.3170939278246623e-181	2.058561309467564e-162	8.166050102475927e-163
10	-5.157736219728953e-293	2.8618744000636808e-307	-2.3629273245375e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	54
1	82	54

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1972×	body	1280	invalid
866.0ms	7542×	body	80	valid
651.0ms	1286×	body	640	invalid
188.0ms	533×	body	320	invalid
95.0ms	126×	body	1280	valid
86.0ms	165×	body	640	valid
53.0ms	225×	body	160	invalid
50.0ms	431×	body	80	invalid
39.0ms	109×	body	320	valid
14.0ms	58×	body	160	valid

Details

analyze1.5s

sample138.0ms

simplify467.0ms

prune28.0ms

localize25.0ms

rewrite22.0ms

series85.0ms

simplify46.0ms

prune121.0ms

localize16.0ms

rewrite18.0ms

series73.0ms

simplify49.0ms

prune118.0ms

localize12.0ms

rewrite17.0ms

series64.0ms

simplify55.0ms

prune97.0ms

localize29.0ms

rewrite25.0ms

series161.0ms

simplify41.0ms

prune83.0ms

regimes541.0ms

bsearch262.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling