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

sample157.0ms

Algorithm

intervals

Results

58.0ms	72×	body	1280	invalid
31.0ms	57×	body	640	invalid
29.0ms	244×	body	80	valid
6.0ms	17×	body	320	invalid
4.0ms	5×	body	1280	valid
2.0ms	8×	body	160	invalid
2.0ms	13×	body	80	invalid
2.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify461.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune24.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) y.im)
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.4b	(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)))

series83.0ms

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)))
66.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	677

prune117.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 16.9b

Counts

69 → 4

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)
0.8b	(* (atan2 x.im x.re) y.im)
28.7b	(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)))

series72.0ms

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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4931	892
1	4931	892

prune113.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 3.0b

Counts

81 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) y.im)
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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

series69.0ms

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

simplify42.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5029	677

prune111.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 3.0b

Counts

73 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.4b	(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)))
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)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(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)))
50.0ms	(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

prune78.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	51	5	56

Merged error: 3.0b

Counts

56 → 5

regimes405.0ms

Accuracy

79.2% (6.2b remaining)

Error of 9.7b against oracle of 3.6b and baseline of 33.2b

bsearch243.0ms

Steps

Iters	Range	Point
8	-3.7591087908186454e-308	1.799430090699395e-305	2.6534303601141e-310
7	-2.626930248556243e-251	-1.546630436647418e-252	-1.224739100076943e-251
9	-8.024628315581496e-220	-4.941262015845708e-227	-5.040043558198871e-227

Iters

Range

Point

-3.7591087908186454e-308

1.799430090699395e-305

2.6534303601141e-310

-2.626930248556243e-251

-1.546630436647418e-252

-1.224739100076943e-251

-8.024628315581496e-220

-4.941262015845708e-227

-5.040043558198871e-227

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	67
1	81	67

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1963×	body	1280	invalid
894.0ms	7564×	body	80	valid
672.0ms	1310×	body	640	invalid
194.0ms	537×	body	320	invalid
91.0ms	120×	body	1280	valid
76.0ms	149×	body	640	valid
56.0ms	232×	body	160	invalid
45.0ms	375×	body	80	invalid
35.0ms	95×	body	320	valid
18.0ms	72×	body	160	valid

Details

analyze1.5s

sample157.0ms

simplify461.0ms

prune24.0ms

localize24.0ms

rewrite22.0ms

series83.0ms

simplify43.0ms

prune117.0ms

localize16.0ms

rewrite18.0ms

series72.0ms

simplify48.0ms

prune113.0ms

localize26.0ms

rewrite19.0ms

series69.0ms

simplify42.0ms

prune111.0ms

localize32.0ms

rewrite24.0ms

series158.0ms

simplify41.0ms

prune78.0ms

regimes405.0ms

bsearch243.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling