Details

analyze1.5s

Algorithm: search

sample153.0ms

Algorithm

intervals

Results

60.0ms	71×	body	1280	invalid
28.0ms	233×	body	80	valid
20.0ms	38×	body	640	invalid
8.0ms	10×	body	1280	valid
5.0ms	13×	body	320	invalid
4.0ms	7×	body	640	valid
2.0ms	1×	body	2560	invalid
2.0ms	15×	body	80	invalid
2.0ms	4×	body	160	invalid
1.0ms	4×	body	160	valid
1.0ms	2×	body	320	valid

simplify393.0ms

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

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: 35.3b

Counts

2 → 2

localize45.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (atan2 x.im x.re) y.im)
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(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)
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)))

series88.0ms

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)))

simplify82.0ms

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

prune164.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 21.7b

Counts

70 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify69.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	156	544
1	346	498
2	780	497
3	2120	497
4	5002	494

prune151.0ms

Filtered

55 candidates to 65 candidates (-18.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	66	10	76

Merged error: 21.7b

Counts

76 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
32.6b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
32.6b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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)))
20.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify69.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	156	832
1	346	718
2	780	715
3	2120	715
4	5002	714

prune142.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	51	10	61

Merged error: 21.7b

Counts

61 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`cbrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `unpow-prod-down` `sin-sum` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

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)))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

series77.0ms

Counts

4 → 12

Calls

4 calls:

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)))
12.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 4 (78.0ms)

Iter	Nodes	Cost
0	211	456
1	537	424
2	1142	423
3	2771	423
4	5001	421

prune116.0ms

Filtered

55 candidates to 67 candidates (-21.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	67	10	77

Merged error: 21.7b

Counts

77 → 10

regimes508.0ms

Accuracy

73.7% (3.8b remaining)

Error of 23.3b against oracle of 19.5b and baseline of 33.9b

bsearch3.8s

Steps

Iters	Range		Point
8	4.9972004847091636e+76	4.4498641221023124e+80	5.071550468219113e+76
8	1.1067923923457705e-64	3.0231721093770095e-61	2.841576465950596e-64
10	-2.0312716467082546e-296	2.6773387154964622e-306	-2.78232521354766e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	75
1	63	75

end0.0ms

analyze1.3s

Algorithm: search

sample4.0s

Algorithm

intervals

Results

1.6s	2038×	body	1280	invalid
882.0ms	7546×	body	80	valid
619.0ms	1225×	body	640	invalid
154.0ms	438×	body	320	invalid
95.0ms	127×	body	1280	valid
82.0ms	165×	body	640	valid
70.0ms	42×	body	2560	invalid
50.0ms	400×	body	80	invalid
44.0ms	189×	body	160	invalid
36.0ms	102×	body	320	valid
15.0ms	60×	body	160	valid

Details

analyze1.5s

sample153.0ms

simplify393.0ms

prune19.0ms

localize45.0ms

rewrite21.0ms

series88.0ms

simplify82.0ms

prune164.0ms

localize29.0ms

rewrite29.0ms

series74.0ms

simplify69.0ms

prune151.0ms

localize39.0ms

rewrite59.0ms

series171.0ms

simplify69.0ms

prune142.0ms

localize26.0ms

rewrite17.0ms

series77.0ms

simplify84.0ms

prune116.0ms

regimes508.0ms

bsearch3.8s

simplify2.0ms

end0.0ms

analyze1.3s

sample4.0s

Profiling