Details

sample431.0ms

Algorithm

intervals

Results

46.0ms	68×	body	1280	valid
46.0ms	254×	body	80	valid
29.0ms	57×	body	640	valid
9.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify45.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.8b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(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:

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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (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)))
153.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2494	381
4	5002	381

prune292.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 15.7b

Counts

69 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
2.7b	(* (atan2 x.im x.re) y.im)
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (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)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
88.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	290	541
1	897	501
2	2715	491
3	5001	491

prune231.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Merged error: 5.0b

Counts

82 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (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)))

rewrite30.0ms

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×	`cos-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)))
17.0ms	(cos (+ (* (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)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
139.0ms	(cos (+ (* (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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	141	530
1	308	486
2	714	486
3	1904	486
4	5001	483

prune328.0ms

Filtered

65 candidates to 55 candidates (84.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	65	7	72

Merged error: 5.0b

Counts

72 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
139.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2494	381
4	5002	381

prune305.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	67	8	75

Merged error: 5.0b

Counts

75 → 8

regimes269.0ms

Accuracy

56.3% (7.0b remaining)

Error of 10.6b against oracle of 3.6b and baseline of 19.6b

bsearch153.0ms

Steps

Iters	Range		Point
8	2.0139662473671948e-47	1.0314885363993931e-42	1.0096310117191709e-42
3	-3.4934054418409164e+58	-2.6783226895871096e+58	-2.729265361602973e+58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	52	26
2	52	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2114×	body	1280	valid
835.0ms	8003×	body	80	valid
683.0ms	1478×	body	640	valid
212.0ms	645×	body	320	valid
71.0ms	310×	body	160	valid

Details

sample431.0ms

simplify45.0ms

prune13.0ms

localize32.0ms

rewrite23.0ms

series246.0ms

simplify79.0ms

prune292.0ms

localize16.0ms

rewrite18.0ms

series262.0ms

simplify78.0ms

prune231.0ms

localize27.0ms

rewrite30.0ms

series249.0ms

simplify66.0ms

prune328.0ms

localize25.0ms

rewrite19.0ms

series231.0ms

simplify77.0ms

prune305.0ms

regimes269.0ms

bsearch153.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling