Details

sample12.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.439453%

Guaranteed chance to sample good point: 55.118931%

Results

53.0ms	74×	body	1280	invalid
30.0ms	239×	body	80	valid
29.0ms	60×	body	640	invalid
7.0ms	22×	body	320	invalid
4.0ms	6×	body	1280	valid
2.0ms	10×	body	160	invalid
2.0ms	6×	body	320	valid
2.0ms	9×	body	80	invalid
1.0ms	4×	body	160	valid
0.0ms	1×	body	640	valid

simplify389.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 29.2b

Counts

2 → 2

localize44.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(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 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune131.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 15.5b

Counts

70 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (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)
1.6b	(* (atan2 x.im x.re) y.im)
25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (- (* (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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
25.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune134.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 3.9b

Counts

87 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(cos (+ (* (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

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune126.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Merged error: 3.9b

Counts

76 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

25.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(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

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

series162.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
51.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(cos (+ (* (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

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	145	556
1	305	490
2	651	490
3	1674	490
4	5002	489

prune84.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	51	8	59

Merged error: 3.9b

Counts

59 → 8

regimes535.0ms

Accuracy

75.6% (7.2b remaining)

Error of 11.3b against oracle of 4.1b and baseline of 33.5b

bsearch328.0ms

Steps

Iters	Range		Point
9	2.196159187545125e-33	4.08711801534481e-24	2.4135661748946774e-27
7	8.237005893457182e-160	4.701519354354967e-158	6.96061085206939e-159
10	-2.959959117202119e-304	1.3084225328977292e-300	-3.7573423790582e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	43
1	63	43
2	63	43

end0.0ms

sample16.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.439453%

Guaranteed chance to sample good point: 55.118931%

Results

1.4s	1964×	body	1280	invalid
825.0ms	7507×	body	80	valid
643.0ms	1355×	body	640	invalid
190.0ms	563×	body	320	invalid
99.0ms	138×	body	1280	valid
84.0ms	173×	body	640	valid
60.0ms	259×	body	160	invalid
41.0ms	364×	body	80	invalid
35.0ms	105×	body	320	valid
17.0ms	77×	body	160	valid

Details

sample12.7s

simplify389.0ms

prune19.0ms

localize44.0ms

rewrite21.0ms

series86.0ms

simplify79.0ms

prune131.0ms

localize16.0ms

rewrite18.0ms

series75.0ms

simplify58.0ms

prune134.0ms

localize26.0ms

rewrite20.0ms

series69.0ms

simplify82.0ms

prune126.0ms

localize28.0ms

rewrite23.0ms

series162.0ms

simplify60.0ms

prune84.0ms

regimes535.0ms

bsearch328.0ms

simplify2.0ms

end0.0ms

sample16.7s

Profiling