Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample66.0ms

Algorithm

intervals

Results

22.0ms	202×	body	80	valid
13.0ms	22×	body	2560	valid
6.0ms	13×	body	1280	valid
3.0ms	8×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune25.0ms

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: 33.3b

Counts

2 → 1

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
23.5b	(sqrt (+ (* re re) (* im im)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
60.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
55.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (+ (* re re) (* im im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
62.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify692.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (561.0ms)

Iter	Nodes	Cost
0	4941	1043
1	4941	1043

prune1.2s

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 15.3b

Counts

64 → 7

localize144.0ms

Local error

Found 4 expressions with local error:

9.1b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

139.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
15.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
58.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify605.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (489.0ms)

Iter	Nodes	Cost
0	5311	928

prune1.1s

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Merged error: 15.3b

Counts

75 → 8

localize145.0ms

Local error

Found 4 expressions with local error:

12.5b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

144.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
28.0ms	(sqrt (+ (* re re) (* im im)))
19.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
96.0ms	(sqrt (+ (* re re) (* im im)))
79.0ms	(sqrt (+ (* re re) (* im im)))
71.0ms	(sqrt (+ (* re re) (* im im)))

simplify659.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (521.0ms)

Iter	Nodes	Cost
0	5149	928

prune923.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	68	8	76

Merged error: 15.3b

Counts

76 → 8

localize95.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))
23.5b	(sqrt (+ (* re re) (* im im)))
24.5b	(cbrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

12.0ms	(sqrt (+ (* re re) (* im im)))
21.0ms	(sqrt (+ (* re re) (* im im)))
18.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(cbrt (+ (* re re) (* im im)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (+ (* re re) (* im im)))
23.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
195.0ms	(cbrt (+ (* re re) (* im im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5176	1030

prune680.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	69	9	78

Merged error: 15.3b

Counts

78 → 9

regimes1.6s

Accuracy

57.8% (9.3b remaining)

Error of 26.2b against oracle of 16.9b and baseline of 39.0b

bsearch113.0ms

Steps

Iters	Range		Point
7	1.2955668342311733e+65	2.8879612466963344e+66	2.858449367873232e+66
9	6.605843802129455e-301	4.6517981240605297e-293	6.700946626241751e-301

simplify11.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	51	112
1	51	112

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.9s	6052×	body	80	valid
1.3s	716×	body	2560	valid
651.0ms	501×	body	1280	valid
574.0ms	277×	body	5120	valid
258.0ms	268×	body	640	valid
88.0ms	124×	body	320	valid
60.0ms	62×	body	160	valid

Details

analyze2.3s

sample66.0ms

simplify31.0ms

prune25.0ms

localize47.0ms

rewrite165.0ms

series335.0ms

simplify692.0ms

prune1.2s

localize144.0ms

rewrite245.0ms

series219.0ms

simplify605.0ms

prune1.1s

localize145.0ms

rewrite239.0ms

series360.0ms

simplify659.0ms

prune923.0ms

localize95.0ms

rewrite78.0ms

series268.0ms

simplify121.0ms

prune680.0ms

regimes1.6s

bsearch113.0ms

simplify11.0ms

end0.0ms

sample5.9s

Profiling