Details

sample172.0ms

Algorithm

intervals

Results

70.0ms	849×	body	80	nan
29.0ms	343×	body	80	valid
17.0ms	28×	body	1280	nan
10.0ms	69×	body	80	overflowed
10.0ms	22×	body	640	nan
3.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify38.0ms

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: 0.4b

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

rewrite35.0ms

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

series549.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
45.0ms	(/ 1.0 (sqrt k))
34.0ms	(* (* 2.0 PI) n)

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5002	1383

prune440.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	11	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Merged error: 0.0b

Counts

170 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
15.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
905.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)

simplify104.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	935	1406
1	4012	1247
2	5001	1237

prune274.0ms

Filtered

138 candidates to 67 candidates (48.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	138	11	149

Merged error: 0b

Counts

149 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 217

Calls

4 calls:

28.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series905.0ms

Counts

4 → 12

Calls

4 calls:

794.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
38.0ms	(/ 1.0 (sqrt k))
39.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)

simplify57.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1308	2682
1	5001	2469

prune496.0ms

Filtered

229 candidates to 135 candidates (59.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	229	11	240

Merged error: 0b

Counts

240 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
27×	`add-sqr-sqrt`
26×	`sqrt-prod`
21×	`add-exp-log` `add-cbrt-cube`
17×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-prod-down`
11×	`associate-l`
10×	`swap-sqr` `prod-exp` `cbrt-unprod`
8×	`sqrt-pow1` `pow1/2`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `times-frac` `sqrt-div` `*-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 120

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
17.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
34.0ms	(* (* 2.0 PI) n)
1.2s	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	658	1713
1	3357	1460
2	5002	1368

prune324.0ms

Filtered

132 candidates to 76 candidates (57.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	132	11	143

Merged error: 0b

Counts

143 → 11

regimes172.0ms

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	19	12
1	19	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	26999×	body	80	nan
911.0ms	10689×	body	80	valid
632.0ms	1047×	body	1280	nan
368.0ms	817×	body	640	nan
337.0ms	2382×	body	80	overflowed
131.0ms	419×	body	320	nan
30.0ms	175×	body	160	nan