Details

sample327.0ms

Algorithm

intervals

Results

22.0ms	251×	body	80	valid
10.0ms	133×	body	80	overflowed
4.0ms	7×	body	1280	valid
3.0ms	6×	body	640	valid
1.0ms	3×	body	320	valid

simplify38.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize34.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
31.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify72.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	189	422
1	491	385
2	1112	381
3	2393	381
4	5001	381

prune306.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

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))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite38.0ms

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:

8.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
82.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	290	540
1	897	500
2	2667	491
3	5002	491

prune257.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
128.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
122.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
124.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify161.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	137	538
1	283	472
2	606	472
3	1518	472
4	4761	471
5	5001	471

prune331.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize28.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 46

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
124.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
121.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify158.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	137	494
1	283	446
2	606	446
3	1518	446
4	4761	442
5	5001	442

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes269.0ms

Accuracy

62.2% (5.9b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 19.3b

bsearch115.0ms

Steps

Iters	Range		Point
6	1.1094921459945167e-45	1.7187035129121457e-44	1.8121822807764002e-45
8	-3.715420481157087e-287	-1.0080192319600841e-289	-1.5826145980796775e-289

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	27
1	68	27
2	68	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

645.0ms	7977×	body	80	valid
320.0ms	3940×	body	80	overflowed
89.0ms	138×	body	1280	valid
63.0ms	163×	body	640	valid
31.0ms	108×	body	320	valid
11.0ms	63×	body	160	valid