Details

analyze1.6s

Algorithm: search

sample137.0ms

Algorithm

intervals

Results

50.0ms	58×	body	1280	invalid
31.0ms	243×	body	80	valid
18.0ms	33×	body	640	invalid
7.0ms	18×	body	320	invalid
3.0ms	4×	body	1280	valid
2.0ms	5×	body	320	valid
2.0ms	1×	body	2560	invalid
2.0ms	3×	body	640	valid
2.0ms	12×	body	80	invalid
0.0ms	1×	body	160	invalid
0.0ms	1×	body	160	valid

simplify406.0ms

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

prune20.0ms

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: 33.1b

Counts

2 → 2

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

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

series89.0ms

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)))
71.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune141.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 17.6b

Counts

70 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (atan2 x.im x.re))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune131.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	60	8	68

Merged error: 17.6b

Counts

68 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (atan2 x.im x.re))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune127.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 17.6b

Counts

69 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

6.1b	(log (exp (cbrt (atan2 x.im x.re))))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

3.0ms	(log (exp (cbrt (atan2 x.im x.re))))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(log (exp (cbrt (atan2 x.im x.re))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sin (+ (* (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: 4 (66.0ms)

Iter	Nodes	Cost
0	198	452
1	403	407
2	844	404
3	2297	404
4	5001	402

prune92.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Merged error: 17.6b

Counts

75 → 7

regimes405.0ms

Accuracy

78.4% (3.1b remaining)

Error of 22.3b against oracle of 19.2b and baseline of 33.7b

bsearch1.4s

Steps

Iters	Range		Point
8	-3.9727907335540565e-306	8.751989257076327e-307	-5.7950528508698e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

analyze1.3s

Algorithm: search

sample4.2s

Algorithm

intervals

Results

1.7s	2130×	body	1280	invalid
915.0ms	7547×	body	80	valid
665.0ms	1251×	body	640	invalid
174.0ms	476×	body	320	invalid
97.0ms	127×	body	1280	valid
85.0ms	159×	body	640	valid
73.0ms	43×	body	2560	invalid
50.0ms	383×	body	80	invalid
41.0ms	170×	body	160	invalid
41.0ms	110×	body	320	valid
14.0ms	57×	body	160	valid

Details

analyze1.6s

sample137.0ms

simplify406.0ms

prune20.0ms

localize47.0ms

rewrite22.0ms

series89.0ms

simplify81.0ms

prune141.0ms

localize28.0ms

rewrite18.0ms

series76.0ms

simplify73.0ms

prune131.0ms

localize33.0ms

rewrite15.0ms

series78.0ms

simplify71.0ms

prune127.0ms

localize34.0ms

rewrite17.0ms

series77.0ms

simplify72.0ms

prune92.0ms

regimes405.0ms

bsearch1.4s

simplify2.0ms

end0.0ms

analyze1.3s

sample4.2s

Profiling