Details

sample363.0ms

Algorithm

intervals

Results

36.0ms	60×	body	1280	valid
24.0ms	255×	body	80	valid
14.0ms	36×	body	640	valid
5.0ms	19×	body	320	valid
2.0ms	9×	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

prune35.0ms

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: 33.7b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(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)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(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	422
1	501	385
2	1134	381
3	2496	381
4	5001	381

prune334.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 20.0b

Counts

70 → 6

localize17.0ms

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)
1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

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))
6.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
96.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (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	540
1	897	500
2	2667	491
3	5002	491

prune272.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 4.1b

Counts

84 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(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:

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

series234.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
138.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

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	2496	381
4	5001	381

prune370.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 4.1b

Counts

76 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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:

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

series464.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
138.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
143.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
141.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify164.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (53.0ms)

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

prune375.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Merged error: 4.1b

Counts

58 → 8

regimes405.0ms

Accuracy

80.5% (5.9b remaining)

Error of 9.4b against oracle of 3.5b and baseline of 33.7b

bsearch354.0ms

Steps

Iters	Range	Point
9	-1.2049654802029013e-301	1.5653172648300943e-307	-4.1709130697605e-310
8	-2.285123779241871e-144	-1.6487772658534058e-147	-1.8398662980718378e-144
9	-5.4829136341776475e-08	-6.297457680062188e-14	-8.307602753419892e-13

Iters

Range

Point

-1.2049654802029013e-301

1.5653172648300943e-307

-4.1709130697605e-310

-2.285123779241871e-144

-1.6487772658534058e-147

-1.8398662980718378e-144

-5.4829136341776475e-08

-6.297457680062188e-14

-8.307602753419892e-13

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	61
1	68	61
2	68	61

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1969×	body	1280	valid
673.0ms	7977×	body	80	valid
577.0ms	1472×	body	640	valid
171.0ms	650×	body	320	valid
52.0ms	294×	body	160	valid

Details

sample363.0ms

simplify40.0ms

prune35.0ms

localize26.0ms

rewrite23.0ms

series256.0ms

simplify77.0ms

prune334.0ms

localize17.0ms

rewrite22.0ms

series283.0ms

simplify78.0ms

prune272.0ms

localize30.0ms

rewrite19.0ms

series234.0ms

simplify76.0ms

prune370.0ms

localize36.0ms

rewrite26.0ms

series464.0ms

simplify164.0ms

prune375.0ms

regimes405.0ms

bsearch354.0ms

simplify3.0ms

end0.0ms

sample3.0s

Profiling