Details

sample134.0ms

Algorithm

intervals

Results

48.0ms	810×	body	80	nan
21.0ms	334×	body	80	valid
16.0ms	46×	body	1280	nan
16.0ms	60×	body	640	nan
3.0ms	15×	body	320	nan
2.0ms	14×	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: 0.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

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

series545.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
324.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5001	1383

prune428.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 0b

Counts

170 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
31.0ms	(* (* 2.0 PI) n)
39.0ms	(* (* 2.0 PI) n)
893.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify109.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (87.0ms)

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

prune263.0ms

Filtered

138 candidates to 68 candidates (49.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	138	9	147

Merged error: 0b

Counts

147 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
21×	`add-cbrt-cube`
14×	`pow1`
11×	`associate-r`
8×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 137

Calls

4 calls:

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

series608.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
495.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	608	1054
1	2498	949
2	5001	932

prune356.0ms

Filtered

149 candidates to 101 candidates (67.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	149	9	158

Merged error: 0b

Counts

158 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
50×	`add-sqr-sqrt`
39×	`prod-exp`
37×	`*-un-lft-identity` `times-frac`
31×	`add-cube-cbrt`
28×	`pow1`
24×	`associate-l`
23×	`add-cbrt-cube`
19×	`pow-unpow`
17×	`associate-r` `sqrt-prod`
15×	`pow-prod-down`
12×	`pow-exp`
11×	`cbrt-unprod`
6×	`div-exp` `unswap-sqr`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `div-sub` `*-commutative` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`unpow-prod-down` `div-inv`
1×	`cbrt-undiv` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 149

Calls

4 calls:

13.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) (sqrt n))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series661.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
339.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
77.0ms	(* (* 2.0 PI) (sqrt n))
44.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify111.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	1063	1848
1	4473	1609
2	5001	1585

prune497.0ms

Filtered

161 candidates to 106 candidates (65.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	163	7	170

Merged error: 0b

Counts

170 → 7

regimes129.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b 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

sample4.4s

Algorithm

intervals

Results

1.5s	26658×	body	80	nan
717.0ms	1959×	body	1280	nan
682.0ms	10632×	body	80	valid
466.0ms	1689×	body	640	nan
164.0ms	844×	body	320	nan
51.0ms	441×	body	160	nan