Details

sample181.0ms

Algorithm

intervals

Results

62.0ms	804×	body	80	nan
33.0ms	321×	body	80	valid
24.0ms	40×	body	1280	nan
11.0ms	76×	body	80	overflowed
10.0ms	23×	body	640	nan
3.0ms	11×	body	320	nan
1.0ms	4×	body	160	nan

simplify34.0ms

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 (100.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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))
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))
5.0ms	(* (* 2.0 PI) n)

series87.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
57.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
19.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)

simplify105.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	953	1493
1	4234	1364
2	5001	1352

prune323.0ms

Filtered

161 candidates to 107 candidates (33.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	147	14	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	14	162

Merged error: 0b

Counts

162 → 14

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)

rewrite31.0ms

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:

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

series170.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
141.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)

simplify125.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	939	1410
1	4082	1188
2	5001	1188

prune198.0ms

Filtered

130 candidates to 59 candidates (54.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	132	12	144

Merged error: 0b

Counts

144 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
25.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series143.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
129.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)

simplify56.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1280	2683
1	5001	2479

prune426.0ms

Filtered

221 candidates to 127 candidates (42.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	221	12	233

Merged error: 0b

Counts

233 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
28.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) (sqrt n))
5.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify47.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1124	1865
1	5001	1600

prune238.0ms

Filtered

153 candidates to 98 candidates (35.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	3	6	9
Picked	1	0	1
Done	0	2	2
Total	155	10	165

Merged error: 0b

Counts

165 → 10

regimes273.0ms

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	19	12
1	19	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	27185×	body	80	nan
893.0ms	10677×	body	80	valid
647.0ms	1043×	body	1280	nan
379.0ms	847×	body	640	nan
335.0ms	2443×	body	80	overflowed
130.0ms	422×	body	320	nan
35.0ms	198×	body	160	nan

Details

sample181.0ms

simplify34.0ms

prune3.0ms

localize13.0ms

rewrite33.0ms

series87.0ms

simplify105.0ms

prune323.0ms

localize18.0ms

rewrite31.0ms

series170.0ms

simplify125.0ms

prune198.0ms

localize18.0ms

rewrite49.0ms

series143.0ms

simplify56.0ms

prune426.0ms

localize16.0ms

rewrite45.0ms

series98.0ms

simplify47.0ms

prune238.0ms

regimes273.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

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