Details

sample382.0ms

Algorithm

intervals

Results

55.0ms	80×	body	1280	valid
25.0ms	258×	body	80	valid
22.0ms	51×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	7×	body	160	valid

simplify52.0ms

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: 32.1b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`sqrt-div` `swap-sqr` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	193	485
1	488	448
2	1083	448
3	2716	448
4	5001	448

prune287.0ms

Filtered

79 candidates to 55 candidates (69.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Merged error: 18.6b

Counts

81 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
151.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
152.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	139	638
1	278	572
2	575	572
3	1729	572
4	5002	572

prune330.0ms

Filtered

59 candidates to 51 candidates (86.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	58	10	68

Merged error: 18.6b

Counts

68 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`sqrt-div` `swap-sqr` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms	(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

79 → 79

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	193	485
1	488	448
2	1083	448
3	2716	448
4	5001	448

prune280.0ms

Filtered

79 candidates to 55 candidates (69.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	79	10	89

Merged error: 18.6b

Counts

89 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

12.8b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
16×	`sqrt-prod`
10×	`add-sqr-sqrt` `distribute-lft-out`
8×	`cbrt-prod` `add-cube-cbrt` `associate-l`
6×	`pow1`
4×	`add-exp-log` `sqrt-div` `swap-sqr` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `rem-cbrt-cube` `flip-+`
1×	`+-commutative` `pow-unpow` `pow1/3` `unpow3` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

17.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify134.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 4 (125.0ms)

Iter	Nodes	Cost
0	182	690
1	435	681
2	1069	681
3	3873	681
4	5002	631

prune271.0ms

Filtered

79 candidates to 54 candidates (68.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	80	9	89

Merged error: 18.6b

Counts

89 → 9

regimes316.0ms

Accuracy

78.8% (3.0b remaining)

Error of 22.7b against oracle of 19.6b and baseline of 33.9b

bsearch149.0ms

Steps

Iters	Range		Point
10	-2.2947903752997222e-302	2.2762297762839958e-302	-5.186698545957517e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	42	36

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2244×	body	1280	valid
702.0ms	7932×	body	80	valid
614.0ms	1447×	body	640	valid
177.0ms	578×	body	320	valid
66.0ms	44×	body	2560	valid
46.0ms	241×	body	160	valid