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

53.0ms	68×	body	1280	invalid
29.0ms	247×	body	80	valid
22.0ms	45×	body	640	invalid
5.0ms	16×	body	320	invalid
2.0ms	8×	body	160	invalid
2.0ms	5×	body	320	valid
1.0ms	3×	body	640	valid
1.0ms	12×	body	80	invalid
1.0ms	1×	body	1280	valid

simplify463.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4897	36
1	4897	36

prune21.0ms

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: 33.7b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (atan2 x.im x.re) y.re)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(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.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(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.re)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5027	676

prune130.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 19.0b

Counts

70 → 4

localize17.0ms

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.4b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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

Counts

4 → 68

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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(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)))

simplify29.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5043	842

prune141.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Merged error: 2.1b

Counts

84 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (pow (exp (atan2 x.im x.re)) (neg y.im)))
0.5b	(exp (atan2 x.im x.re))
1.2b	(pow (exp (atan2 x.im x.re)) (neg y.im))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
12×	`unswap-sqr`
10×	`pow-unpow` `associate-l` `sqr-pow`
9×	`prod-exp` `sqrt-prod`
7×	`pow-to-exp` `associate-r` `pow-exp`
6×	`pow1` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`pow-pow`
3×	`distribute-lft-neg-in` `pow-neg` `distribute-rgt-neg-in`
2×	`neg-sub0` `sqrt-div` `associate-*r/` `pow-sub`
1×	`neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `un-div-inv` `*-commutative` `cbrt-unprod` `flip-+` `rem-exp-log`

Counts

4 → 105

Calls

4 calls:

12.0ms	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (pow (exp (atan2 x.im x.re)) (neg y.im)))
2.0ms	(exp (atan2 x.im x.re))
4.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (pow (exp (atan2 x.im x.re)) (neg y.im)))
4.0ms	(exp (atan2 x.im x.re))
12.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5165	1677

prune146.0ms

Filtered

80 candidates to 117 candidates (-46.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	117	6	123

Merged error: 2.1b

Counts

123 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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)))
9.0ms	(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)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(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)))
49.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4962	812
1	4962	812

prune91.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	49	8	57

Merged error: 2.1b

Counts

57 → 8

regimes454.0ms

Accuracy

67.1% (5.4b remaining)

Error of 8.8b against oracle of 3.5b and baseline of 19.7b

bsearch248.0ms

Steps

Iters	Range		Point
9	6.394553194570509e-69	7.241031404090824e-63	7.027221242821304e-68
9	1.3877518063409838e-167	2.069871222658754e-158	3.4498780821159295e-165
10	-4.123054802319074e-306	3.441803137792769e-300	1.2023040272701e-310

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	158	54
1	158	54

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1932×	body	1280	invalid
857.0ms	7573×	body	80	valid
646.0ms	1351×	body	640	invalid
190.0ms	545×	body	320	invalid
93.0ms	131×	body	1280	valid
70.0ms	142×	body	640	valid
56.0ms	249×	body	160	invalid
49.0ms	408×	body	80	invalid
32.0ms	93×	body	320	valid
14.0ms	61×	body	160	valid

Details

analyze1.5s

sample138.0ms

simplify463.0ms

prune21.0ms

localize24.0ms

rewrite22.0ms

series85.0ms

simplify59.0ms

prune130.0ms

localize17.0ms

rewrite18.0ms

series73.0ms

simplify29.0ms

prune141.0ms

localize16.0ms

rewrite24.0ms

series66.0ms

simplify44.0ms

prune146.0ms

localize27.0ms

rewrite26.0ms

series154.0ms

simplify57.0ms

prune91.0ms

regimes454.0ms

bsearch248.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling