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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample151.0ms

Algorithm

intervals

Results

58.0ms	73×	body	1280	invalid
27.0ms	234×	body	80	valid
21.0ms	40×	body	640	invalid
6.0ms	1×	body	2560	invalid
6.0ms	17×	body	320	invalid
3.0ms	4×	body	1280	valid
2.0ms	9×	body	160	valid
2.0ms	4×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	6×	body	160	invalid
1.0ms	9×	body	80	invalid

simplify462.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune35.0ms

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: 34.9b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
29.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`sin-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)
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
65.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5128	689

prune178.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 22.7b

Counts

70 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

29.9b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

Calls

4 calls:

19.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (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)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (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)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5053	721

prune160.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	64	14	78

Merged error: 22.7b

Counts

78 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
29.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`sin-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)
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5096	689

prune151.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	68	14	82

Merged error: 22.7b

Counts

82 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (atan2 x.im x.re))
29.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow1/3`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (atan2 x.im x.re))
62.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4988	635
1	4988	635

prune85.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	61	14	75

Merged error: 22.7b

Counts

75 → 14

regimes603.0ms

Accuracy

71.9% (3.8b remaining)

Error of 23.3b against oracle of 19.4b and baseline of 33.1b

bsearch204.0ms

Steps

Iters	Range		Point
6	-2.2319409480524666e-292	-5.157736219728953e-293	-5.239321828716821e-293
5	-8.124474460648546e-165	-3.669000806034207e-165	-8.044352608599044e-165
8	-217664156687033.22	-102547762882.85402	-127770443998.57332

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	152
1	86	152

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2141×	body	1280	invalid
869.0ms	7533×	body	80	valid
632.0ms	1255×	body	640	invalid
170.0ms	472×	body	320	invalid
99.0ms	134×	body	1280	valid
76.0ms	151×	body	640	valid
72.0ms	42×	body	2560	invalid
49.0ms	395×	body	80	invalid
45.0ms	196×	body	160	invalid
40.0ms	111×	body	320	valid
17.0ms	71×	body	160	valid

Details

analyze1.5s

sample151.0ms

simplify462.0ms

prune35.0ms

localize25.0ms

rewrite22.0ms

series91.0ms

simplify45.0ms

prune178.0ms

localize29.0ms

rewrite33.0ms

series76.0ms

simplify54.0ms

prune160.0ms

localize29.0ms

rewrite21.0ms

series83.0ms

simplify44.0ms

prune151.0ms

localize35.0ms

rewrite19.0ms

series85.0ms

simplify42.0ms

prune85.0ms

regimes603.0ms

bsearch204.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling