Details

sample218.0ms

Algorithm

intervals

Results

85.0ms	983×	body	80	nan
39.0ms	346×	body	80	valid
32.0ms	69×	body	1280	nan
20.0ms	54×	body	640	nan
6.0ms	23×	body	320	nan
2.0ms	10×	body	160	nan

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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×	`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 → 149

Calls

4 calls:

21.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
7.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series555.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
38.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344

prune439.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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×	`add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
6.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
8.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series459.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
31.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
264.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	453	528
1	1774	479
2	5002	473

prune308.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
13×	`pow-unpow`
12×	`cbrt-unprod`
9×	`times-frac`
6×	`sqrt-prod`
4×	`pow-pow` `pow-exp` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`pow-to-exp` `unpow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

7.0ms	(* (* 2.0 PI) n)
8.0ms	(* (* 2.0 PI) (sqrt n))
29.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
27.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))

series415.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) n)
71.0ms	(* (* 2.0 PI) (sqrt n))
51.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
254.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	502	607
1	2341	489
2	5002	478

prune296.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
33×	`prod-exp`
28×	`add-sqr-sqrt`
20×	`pow1`
19×	`associate-r`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`pow-exp`
16×	`add-cbrt-cube`
13×	`pow-unpow`
12×	`unpow-prod-down`
10×	`pow-prod-down`
9×	`pow-to-exp` `times-frac` `sqr-pow`
8×	`sqrt-prod` `unswap-sqr`
7×	`associate-l` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-pow` `*-commutative`
1×	`div-inv`

Counts

4 → 116

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
7.0ms	(* (* 2.0 PI) n)
8.0ms	(* (* 2.0 PI) (sqrt n))
13.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
38.0ms	(* (* 2.0 PI) n)
71.0ms	(* (* 2.0 PI) (sqrt n))
915.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	726	1026
1	3053	874
2	5002	870

prune382.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	17
1	25	17

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.3s	26987×	body	80	nan
1.2s	10603×	body	80	valid
977.0ms	1974×	body	1280	nan
635.0ms	1683×	body	640	nan
224.0ms	858×	body	320	nan
58.0ms	368×	body	160	nan
6.0ms	4×	body	10240	exit