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

sample133.0ms

Algorithm

intervals

Results

38.0ms	52×	body	1280	invalid
28.0ms	234×	body	80	valid
20.0ms	39×	body	640	invalid
12.0ms	24×	body	320	invalid
4.0ms	8×	body	640	valid
3.0ms	9×	body	320	valid
3.0ms	4×	body	1280	valid
2.0ms	7×	body	160	invalid
1.0ms	10×	body	80	invalid
0.0ms	1×	body	160	valid

simplify462.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune32.0ms

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: 33.6b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(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

prune141.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 18.2b

Counts

70 → 7

localize20.0ms

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)
1.5b	(* (atan2 x.im x.re) y.im)
28.9b	(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)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4925	844
1	4925	844

prune141.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 5.3b

Counts

87 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow E (- (* (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)
1.5b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `associate-l`
8×	`add-cbrt-cube`
6×	`associate-r`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`unpow-prod-up` `pow-to-exp` `sub-neg` `rem-sqrt-square` `e-exp-1` `pow-pow` `flip3-+` `flip-+` `pow-sub` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

4.0ms	(pow E (- (* (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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow E (- (* (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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4916	1076
1	4916	1076

prune128.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Merged error: 5.3b

Counts

94 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
3.5b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`add-exp-log` `log-pow` `add-cbrt-cube`
7×	`associate-l`
6×	`exp-prod` `associate-r` `sqrt-prod`
4×	`add-log-exp`
3×	`log-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4966	744
1	4966	744

prune102.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	83	7	90

Merged error: 5.3b

Counts

90 → 7

regimes347.0ms

Accuracy

59.5% (6.5b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 19.6b

bsearch163.0ms

Steps

Iters	Range		Point
7	4.168970175432756e-118	3.1240746230710504e-116	1.0544495277901194e-116
10	-9.793731920256713e+18	-310243065.3606954	-314818276.7903757

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	50
1	78	50

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	1843×	body	1280	invalid
862.0ms	7559×	body	80	valid
600.0ms	1220×	body	640	invalid
184.0ms	530×	body	320	invalid
109.0ms	147×	body	1280	valid
72.0ms	141×	body	640	valid
58.0ms	247×	body	160	invalid
49.0ms	420×	body	80	invalid
31.0ms	89×	body	320	valid
15.0ms	64×	body	160	valid

Details

analyze1.5s

sample133.0ms

simplify462.0ms

prune32.0ms

localize25.0ms

rewrite21.0ms

series84.0ms

simplify43.0ms

prune141.0ms

localize20.0ms

rewrite18.0ms

series70.0ms

simplify40.0ms

prune141.0ms

localize18.0ms

rewrite18.0ms

series75.0ms

simplify53.0ms

prune128.0ms

localize17.0ms

rewrite20.0ms

series39.0ms

simplify53.0ms

prune102.0ms

regimes347.0ms

bsearch163.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling