Details

sample400.0ms

Algorithm

intervals

Results

58.0ms	86×	body	1280	valid
36.0ms	248×	body	80	valid
27.0ms	64×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	10×	body	160	valid

simplify39.0ms

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

prune15.0ms

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: 33.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

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)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(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)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	199	485
1	509	448
2	1161	448
3	2955	448
4	5001	448

prune326.0ms

Filtered

79 candidates to 55 candidates (69.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 19.9b

Counts

81 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(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)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
138.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	373	844
1	1274	763
2	5002	741

prune471.0ms

Filtered

117 candidates to 75 candidates (64.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Merged error: 19.9b

Counts

124 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

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.re)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	197	485
1	499	448
2	1139	448
3	2834	448
4	5001	448

prune386.0ms

Filtered

79 candidates to 55 candidates (69.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Merged error: 19.9b

Counts

86 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

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:

16.0ms	(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)))
20.0ms	(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)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
137.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
138.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	145	638
1	299	572
2	649	572
3	1965	572
4	5001	572

prune397.0ms

Filtered

59 candidates to 51 candidates (86.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Merged error: 19.8b

Counts

65 → 8

regimes352.0ms

Accuracy

65.9% (4.8b remaining)

Error of 24.6b against oracle of 19.8b and baseline of 33.8b

bsearch290.0ms

Steps

Iters	Range		Point
9	4.890671844991377e-60	2.803383669958892e-52	5.62997084490378e-54
9	-5.4608645180661643e-185	-3.9089750989843753e-193	-4.834691035096915e-189

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	129
1	61	129

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2171×	body	1280	valid
710.0ms	7944×	body	80	valid
575.0ms	1391×	body	640	valid
154.0ms	542×	body	320	valid
73.0ms	48×	body	2560	valid
47.0ms	238×	body	160	valid