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

sample153.0ms

Algorithm

intervals

Results

48.0ms	65×	body	1280	invalid
32.0ms	244×	body	80	valid
29.0ms	57×	body	640	invalid
8.0ms	5×	body	2560	invalid
5.0ms	13×	body	320	invalid
4.0ms	6×	body	1280	valid
2.0ms	16×	body	80	invalid
1.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	invalid

simplify470.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune19.0ms

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: 30.9b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.5b	(sin (+ (* (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×	`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)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series90.0ms

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)))
72.0ms	(sin (+ (* (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	5069	689

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: 15.6b

Counts

70 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.5b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
129.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify50.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4881	889
1	4881	889

prune153.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	59	9	68

Merged error: 15.6b

Counts

68 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
127.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4859	889
1	4859	889

prune148.0ms

Filtered

50 candidates to 61 candidates (-22.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 15.6b

Counts

70 → 8

localize34.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.5b	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
127.0ms	(sin (+ (* (log (* (fabs (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4859	889
1	4859	889

prune106.0ms

Filtered

50 candidates to 61 candidates (-22.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Merged error: 15.6b

Counts

69 → 8

regimes436.0ms

Accuracy

77% (3.3b remaining)

Error of 22.1b against oracle of 18.9b and baseline of 33.0b

bsearch70.0ms

Steps

Iters	Range		Point
6	-3.7591087908186454e-308	5.055916371285476e-308	3.1453924753302e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2154×	body	1280	invalid
829.0ms	7550×	body	80	valid
633.0ms	1276×	body	640	invalid
157.0ms	460×	body	320	invalid
99.0ms	141×	body	1280	valid
72.0ms	147×	body	640	valid
62.0ms	39×	body	2560	invalid
43.0ms	381×	body	80	invalid
36.0ms	164×	body	160	invalid
33.0ms	99×	body	320	valid
14.0ms	63×	body	160	valid

Details

analyze1.5s

sample153.0ms

simplify470.0ms

prune19.0ms

localize25.0ms

rewrite22.0ms

series90.0ms

simplify43.0ms

prune141.0ms

localize30.0ms

rewrite23.0ms

series176.0ms

simplify50.0ms

prune153.0ms

localize34.0ms

rewrite28.0ms

series173.0ms

simplify64.0ms

prune148.0ms

localize34.0ms

rewrite28.0ms

series174.0ms

simplify67.0ms

prune106.0ms

regimes436.0ms

bsearch70.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling