Details

sample138.0ms

Algorithm

intervals

Results

46.0ms	810×	body	80	nan
21.0ms	334×	body	80	valid
20.0ms	46×	body	1280	nan
16.0ms	60×	body	640	nan
3.0ms	15×	body	320	nan
2.0ms	14×	body	160	nan

simplify36.0ms

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	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: 0.4b

Counts

2 → 1

localize13.0ms

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)))

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×	`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:

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)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
328.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify104.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5001	1344

prune379.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	152	9	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	9	162

Merged error: 0b

Counts

162 → 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` `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 → 118

Calls

4 calls:

7.0ms	(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:

259.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)
887.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5001	1199

prune234.0ms

Filtered

130 candidates to 60 candidates (46.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	130	9	139

Merged error: 0b

Counts

139 → 9

localize18.0ms

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)))

rewrite33.0ms

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×	`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 → 129

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
494.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	590	1020
1	2449	915
2	5001	905

prune320.0ms

Filtered

141 candidates to 93 candidates (66.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	141	9	150

Merged error: 0b

Counts

150 → 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))

rewrite46.0ms

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×	`pow-pow` `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 → 141

Calls

4 calls:

13.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
12.0ms	(* (/ 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))

series660.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
329.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
76.0ms	(* (* 2.0 PI) (sqrt n))
51.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify107.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	1032	1788
1	4370	1548
2	5002	1521

prune317.0ms

Filtered

153 candidates to 96 candidates (62.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	155	7	162

Merged error: 0b

Counts

162 → 7

regimes130.0ms

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

sample4.6s

Algorithm

intervals

Results

1.7s	26658×	body	80	nan
723.0ms	1959×	body	1280	nan
659.0ms	10632×	body	80	valid
452.0ms	1689×	body	640	nan
165.0ms	844×	body	320	nan
52.0ms	441×	body	160	nan