Details

analyze1.5s

Algorithm: search

sample150.0ms

Algorithm

intervals

Results

52.0ms	70×	body	1280	invalid
30.0ms	49×	body	640	invalid
29.0ms	247×	body	80	valid
5.0ms	15×	body	320	invalid
4.0ms	2×	body	2560	invalid
3.0ms	5×	body	640	valid
2.0ms	14×	body	80	invalid
1.0ms	4×	body	160	invalid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify394.0ms

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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 31.0b

Counts

2 → 1

localize45.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sin (+ (* (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×	`sin-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)
3.0ms	(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)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(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

prune126.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 18.9b

Counts

69 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(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

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:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	204	434
1	529	395
2	1179	392
3	2603	392
4	5002	392

prune111.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Merged error: 18.9b

Counts

73 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.5b	(sin (+ (* (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×	`sin-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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

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)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune103.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	51	6	57

Merged error: 18.9b

Counts

57 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
19.3b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 59

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	260	372
1	715	332
2	1646	328
3	3711	328
4	5001	328

prune105.0ms

Filtered

51 candidates to 71 candidates (-39.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	70	7	77

Merged error: 12.0b

Counts

77 → 7

regimes449.0ms

Accuracy

75.1% (5.1b remaining)

Error of 17.7b against oracle of 12.6b and baseline of 33.0b

bsearch2.9s

Steps

Iters	Range		Point
11	-5.1168484212707975e-300	1.6231234508257573e-295	-2.9599460509191e-311
7	-0.7772498620223653	-0.016192012692394665	-0.45001420648911095

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	50
1	51	50

end0.0ms

analyze1.3s

Algorithm: search

sample4.1s

Algorithm

intervals

Results

1.6s	2150×	body	1280	invalid
864.0ms	7543×	body	80	valid
670.0ms	1308×	body	640	invalid
159.0ms	457×	body	320	invalid
99.0ms	57×	body	2560	invalid
99.0ms	136×	body	1280	valid
75.0ms	148×	body	640	valid
52.0ms	428×	body	80	invalid
41.0ms	177×	body	160	invalid
40.0ms	100×	body	320	valid
17.0ms	73×	body	160	valid

Details

analyze1.5s

sample150.0ms

simplify394.0ms

prune15.0ms

localize45.0ms

rewrite21.0ms

series89.0ms

simplify81.0ms

prune126.0ms

localize26.0ms

rewrite17.0ms

series73.0ms

simplify76.0ms

prune111.0ms

localize29.0ms

rewrite23.0ms

series169.0ms

simplify61.0ms

prune103.0ms

localize27.0ms

rewrite18.0ms

series56.0ms

simplify105.0ms

prune105.0ms

regimes449.0ms

bsearch2.9s

simplify2.0ms

end0.0ms

analyze1.3s

sample4.1s

Profiling