Details

sample401.0ms

Algorithm

intervals

Results

43.0ms	59×	body	1280	valid
32.0ms	262×	body	80	valid
30.0ms	61×	body	640	valid
5.0ms	14×	body	320	valid
2.0ms	8×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 33.4b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(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:

4.0ms	(* (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)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2507	386
4	5002	386

prune321.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 18.4b

Counts

70 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (* (atan2 x.im x.re) y.im))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (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)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (* (atan2 x.im x.re) y.im))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1958	373
4	5001	371

prune311.0ms

Filtered

59 candidates to 50 candidates (84.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	59	10	69

Merged error: 18.4b

Counts

69 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (* (atan2 x.im x.re) y.im))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (* (atan2 x.im x.re) y.im))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1958	373
4	5001	371

prune342.0ms

Filtered

59 candidates to 50 candidates (84.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 18.4b

Counts

69 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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:

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)))
23.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	148	607
1	303	551
2	643	551
3	1810	551
4	5001	548

prune319.0ms

Filtered

65 candidates to 56 candidates (86.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	64	10	74

Merged error: 18.4b

Counts

74 → 10

regimes337.0ms

Accuracy

77.1% (3.4b remaining)

Error of 22.5b against oracle of 19.1b and baseline of 33.8b

bsearch425.0ms

Steps

Iters	Range	Point
6	-1.278936478791097e-308	8.023207831786666e-308	-5.156319062013225e-309
11	-1.9611360856757354e-231	-1.558821736665248e-255	-1.9359566382749546e-231
9	-1.0594230812862767e-201	-1.7141606252680141e-208	-2.209948046406341e-208

Iters

Range

Point

-1.278936478791097e-308

8.023207831786666e-308

-5.156319062013225e-309

-1.9611360856757354e-231

-1.558821736665248e-255

-1.9359566382749546e-231

-1.0594230812862767e-201

-1.7141606252680141e-208

-2.209948046406341e-208

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	113
1	65	113

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2128×	body	1280	valid
858.0ms	7944×	body	80	valid
692.0ms	1418×	body	640	valid
188.0ms	565×	body	320	valid
74.0ms	45×	body	2560	valid
58.0ms	263×	body	160	valid

Details

sample401.0ms

simplify40.0ms

prune16.0ms

localize25.0ms

rewrite22.0ms

series254.0ms

simplify78.0ms

prune321.0ms

localize27.0ms

rewrite18.0ms

series282.0ms

simplify65.0ms

prune311.0ms

localize34.0ms

rewrite17.0ms

series277.0ms

simplify64.0ms

prune342.0ms

localize32.0ms

rewrite36.0ms

series253.0ms

simplify65.0ms

prune319.0ms

regimes337.0ms

bsearch425.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling