Details

sample142.0ms

Algorithm

intervals

Results

52.0ms	880×	body	80	nan
22.0ms	343×	body	80	valid
20.0ms	57×	body	1280	nan
11.0ms	43×	body	640	nan
6.0ms	32×	body	320	nan
1.0ms	9×	body	160	nan

simplify41.0ms

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

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: 0.5b

Counts

2 → 1

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
67×	`associate-l`
62×	`add-cube-cbrt`
61×	`times-frac`
53×	`unpow-prod-down`
46×	`add-exp-log`
44×	`associate-r`
36×	`unswap-sqr`
32×	`sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
18×	`associate-/r*`
17×	`pow1`
16×	`add-cbrt-cube`
14×	`div-sub` `pow-sub`
12×	`frac-times` `associate-*l/`
9×	`pow-exp` `associate-/l*`
7×	`pow-prod-down` `*-commutative`
6×	`div-exp`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv`
1×	`associate-*r/`

Counts

4 → 236

Calls

4 calls:

32.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
7.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series559.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
40.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (* 2.0 PI) n)
150.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1241	2334
1	5001	2228

prune727.0ms

Filtered

248 candidates to 170 candidates (68.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	240	8	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	241	8	249

Merged error: 0.0b

Counts

249 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(/ (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

2941×	`add-sqr-sqrt`
2853×	`associate-l`
2342×	`unpow-prod-down`
1842×	`times-frac`
1730×	`associate-r`
1388×	`unswap-sqr`
768×	`add-cube-cbrt` `*-un-lft-identity`
320×	`sqrt-prod`
270×	`*-commutative`
217×	`sqr-pow`
176×	`add-exp-log`
105×	`prod-exp`
47×	`associate-/r*`
39×	`pow-exp` `associate-/l*`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`pow-to-exp` `pow-unpow`
10×	`cbrt-unprod`
9×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow`
2×	`div-inv`
1×	`frac-2neg` `clear-num`

Counts

4 → 2081

Calls

4 calls:

10.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
85.0ms	(/ (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
7.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

257.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
909.0ms	(/ (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
33.0ms	(* (* 2.0 PI) n)
41.0ms	(* (* 2.0 PI) n)

simplify462.0ms

Algorithm

egg-herbie

Counts

2093 → 2093

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5001	45555

prune5.4s

Filtered

2093 candidates to 1264 candidates (60.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	2089	4	2093
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	2095	6	2101

Merged error: 0b

Counts

2101 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.5b	(* (sqrt (* 2.0 PI)) n)
1.0b	(sqrt (* 2.0 PI))
1.0b	(sqrt (* 2.0 PI))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
39×	`associate-l`
38×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-r`
17×	`pow1`
13×	`unswap-sqr`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow-prod-down` `*-commutative`
4×	`rem-sqrt-square` `sqrt-pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`pow1/2`

Counts

4 → 111

Calls

4 calls:

8.0ms	(* (* 2.0 PI) n)
12.0ms	(* (sqrt (* 2.0 PI)) n)
5.0ms	(sqrt (* 2.0 PI))
5.0ms	(sqrt (* 2.0 PI))

series130.0ms

Counts

4 → 8

Calls

4 calls:

33.0ms	(* (* 2.0 PI) n)
97.0ms	(* (sqrt (* 2.0 PI)) n)
0.0ms	(sqrt (* 2.0 PI))
0.0ms	(sqrt (* 2.0 PI))

simplify112.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	257	472
1	1076	449
2	4100	445
3	5002	445

prune412.0ms

Filtered

119 candidates to 86 candidates (72.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	119	6	125

Merged error: 0b

Counts

125 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow 1 (/ 1.0 2.0)) (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0)))
0.2b	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

29356×	`times-frac`
29305×	`add-sqr-sqrt`
26023×	`unpow-prod-down`
24868×	`associate-l`
15133×	`associate-r`
12168×	`unswap-sqr`
10273×	`add-cube-cbrt` `*-un-lft-identity`
3747×	`sqr-pow`
2824×	`sqrt-prod`
2338×	`*-commutative`
1915×	`associate-/r*`
872×	`add-exp-log`
486×	`prod-exp`
328×	`div-exp`
254×	`pow-exp`
101×	`associate-/l*`
97×	`pow-to-exp`
89×	`associate-/r/`
44×	`add-cbrt-cube`
37×	`1-exp`
14×	`pow1` `cbrt-unprod`
13×	`cbrt-undiv`
10×	`div-inv`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`

Counts

4 → 16986

Calls

4 calls:

504.0ms	(/ (pow 1 (/ 1.0 2.0)) (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0)))
85.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0))
7.0ms	(* (* 2.0 PI) n)
10.0ms	(* (* 2.0 PI) n)

series1.7s

Counts

4 → 12

Calls

4 calls:

794.0ms	(/ (pow 1 (/ 1.0 2.0)) (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0)))
846.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0))
39.0ms	(* (* 2.0 PI) n)
34.0ms	(* (* 2.0 PI) n)

simplify5.0s

Algorithm

egg-herbie

Counts

16998 → 16998

Iterations

Useful iterations: 0 (282.0ms)

Iter	Nodes	Cost
0	18806	489414

prune1.1m

Filtered

16998 candidates to 12683 candidates (74.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	16996	2	16998
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	16998	6	17004

Merged error: 0b

Counts

17004 → 6

regimes112.0ms

Accuracy

0% (0.3b 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	27	21
1	27	21

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	27171×	body	80	nan
724.0ms	1989×	body	1280	nan
656.0ms	10634×	body	80	valid
447.0ms	1684×	body	640	nan
157.0ms	829×	body	320	nan
47.0ms	412×	body	160	nan