Details

sample158.0ms

Algorithm

intervals

Results

54.0ms	915×	body	80	nan
29.0ms	86×	body	1280	nan
21.0ms	345×	body	80	valid
13.0ms	49×	body	640	nan
5.0ms	27×	body	320	nan
3.0ms	26×	body	160	nan

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8

prune3.0ms

Filtered

1 candidates to 0 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: 0.7b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 157

Calls

4 calls:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series518.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
33.0ms	(* (* 2.0 PI) n)
36.0ms	(/ 1.0 (sqrt k))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune461.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	155	14	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Merged error: 0.0b

Counts

170 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.2b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log` `pow-unpow`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series438.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
122.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
250.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	463	557
1	1809	510
2	5001	503

prune303.0ms

Filtered

114 candidates to 75 candidates (65.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	114	14	128

Merged error: 0.0b

Counts

128 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.4b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
26×	`pow-unpow`
23×	`sqrt-prod`
22×	`associate-l` `prod-exp`
16×	`pow1`
12×	`pow-exp`
11×	`add-cbrt-cube`
6×	`pow-pow` `div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr` `sqr-pow`
5×	`associate-r`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 159

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
4.0ms	(/ 1.0 (sqrt k))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series895.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
38.0ms	(/ 1.0 (sqrt k))
259.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
480.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	835	1299
1	3252	1207
2	5001	1183

prune470.0ms

Filtered

171 candidates to 120 candidates (70.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	172	13	185

Merged error: 0.0b

Counts

185 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.7b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
68×	`prod-exp`
63×	`add-sqr-sqrt`
55×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
27×	`pow-exp`
23×	`associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`pow-to-exp`
17×	`div-exp`
12×	`associate-r`
11×	`div-sub` `pow-sub`
7×	`pow1` `cbrt-unprod`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 188

Calls

4 calls:

12.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series961.0ms

Counts

4 → 12

Calls

4 calls:

561.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
286.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
76.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify135.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	1162	2113
1	4931	1915
2	5001	1887

prune468.0ms

Filtered

200 candidates to 127 candidates (63.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	197	3	200
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	201	12	213

Merged error: 0.0b

Counts

213 → 12

regimes201.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	26646×	body	80	nan
693.0ms	1948×	body	1280	nan
659.0ms	10619×	body	80	valid
451.0ms	1682×	body	640	nan
169.0ms	903×	body	320	nan
52.0ms	422×	body	160	nan