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

sample195.0ms

Algorithm

intervals

Results

25.0ms	238×	body	80	valid
3.0ms	4×	body	1280	valid
2.0ms	7×	body	320	valid
2.0ms	5×	body	640	valid
0.0ms	2×	body	160	valid

simplify493.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	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: 32.2b

Counts

2 → 2

localize38.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.re)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(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)))

rewrite23.0ms

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:

4.0ms	(* (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)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(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	5098	677

prune126.0ms

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: 19.3b

Counts

70 → 5

localize25.0ms

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)
1.4b	(* (atan2 x.im x.re) y.im)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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:

5.0ms	(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)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (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)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4925	844
1	4925	844

prune140.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	76	9	85

Merged error: 3.8b

Counts

85 → 9

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(exp (atan2 x.im x.re))
2.7b	(pow (exp (atan2 x.im x.re)) y.im)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(log (pow (exp (atan2 x.im x.re)) y.im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
7×	`log-prod`
6×	`pow1` `unpow-prod-down` `exp-prod`
5×	`add-exp-log` `add-log-exp`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp` `sqrt-prod`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `log-pow` `flip-+` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

2.0ms	(exp (atan2 x.im x.re))
4.0ms	(pow (exp (atan2 x.im x.re)) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))

series40.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (atan2 x.im x.re))
13.0ms	(pow (exp (atan2 x.im x.re)) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))

simplify49.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4985	573
1	4985	573

prune126.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	76	9	85

Merged error: 3.8b

Counts

85 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.re)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(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)))

rewrite20.0ms

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:

4.0ms	(* (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)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(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	5098	677

prune111.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	67	10	77

Merged error: 3.8b

Counts

77 → 10

regimes465.0ms

Accuracy

67.8% (5.1b remaining)

Error of 8.6b against oracle of 3.5b and baseline of 19.2b

bsearch85.0ms

Steps

Iters	Range		Point
9	-1.7445426909345827e-308	8.38970250601538e-302	4.89207336018757e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample6.0s

Algorithm

intervals

Results

751.0ms	7569×	body	80	valid
83.0ms	120×	body	1280	valid
71.0ms	155×	body	640	valid
34.0ms	106×	body	320	valid
11.0ms	50×	body	160	valid

Details

analyze1.5s

sample195.0ms

simplify493.0ms

prune21.0ms

localize38.0ms

rewrite23.0ms

series94.0ms

simplify43.0ms

prune126.0ms

localize25.0ms

rewrite20.0ms

series79.0ms

simplify38.0ms

prune140.0ms

localize48.0ms

rewrite14.0ms

series40.0ms

simplify49.0ms

prune126.0ms

localize40.0ms

rewrite20.0ms

series73.0ms

simplify42.0ms

prune111.0ms

regimes465.0ms

bsearch85.0ms

simplify2.0ms

end0.0ms

sample6.0s

Profiling