Details

sample160.0ms

Algorithm

intervals

Results

55.0ms	902×	body	80	nan
25.0ms	70×	body	1280	nan
21.0ms	359×	body	80	valid
16.0ms	62×	body	640	nan
7.0ms	41×	body	320	nan
3.0ms	25×	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	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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

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:

8.0ms	(* (* 2.0 PI) n)
35.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
15.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series545.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
331.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1242	2334
1	5001	2228

prune658.0ms

Filtered

248 candidates to 170 candidates (68.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	239	9	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	240	9	249

Merged error: 0.0b

Counts

249 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

3218×	`associate-r`
3039×	`add-sqr-sqrt`
2827×	`associate-l`
2522×	`unpow-prod-down`
2401×	`times-frac`
1212×	`unswap-sqr`
1118×	`add-cube-cbrt` `*-un-lft-identity`
441×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
306×	`*-commutative`
282×	`sqrt-prod`
201×	`sqr-pow`
176×	`add-exp-log`
105×	`prod-exp`
100×	`neg-mul-1`
52×	`associate-/r*`
46×	`associate-/l*`
39×	`pow-exp`
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×	`distribute-lft-neg-out` `frac-2neg` `distribute-frac-neg` `clear-num`

Counts

4 → 2653

Calls

4 calls:

12.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
201.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
111.0ms	(/ (* (- 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:

268.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
31.0ms	(* (* 2.0 PI) n)
41.0ms	(* (* 2.0 PI) n)
889.0ms	(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify564.0ms

Algorithm

egg-herbie

Counts

2665 → 2665

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5001	61556

prune9.9s

Filtered

2665 candidates to 2046 candidates (76.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	2660	5	2665
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	2668	6	2674

Merged error: 0b

Counts

2674 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify94.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	86	230
1	203	224
2	671	220
3	4138	220
4	5002	220

prune288.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Merged error: 0b

Counts

58 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

4166×	`add-sqr-sqrt`
3787×	`associate-r`
3292×	`unpow-prod-down`
2898×	`times-frac`
2634×	`associate-l`
1661×	`unswap-sqr`
1399×	`add-cube-cbrt` `*-un-lft-identity`
1043×	`cbrt-prod`
474×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
376×	`swap-sqr`
333×	`*-commutative`
282×	`sqrt-prod`
222×	`sqr-pow`
123×	`add-exp-log`
111×	`neg-mul-1`
70×	`prod-exp`
63×	`associate-/r*`
46×	`associate-/l*`
30×	`div-exp`
27×	`pow-exp`
16×	`add-cbrt-cube`
11×	`pow-to-exp`
4×	`pow1` `cbrt-undiv` `cbrt-unprod` `add-log-exp`
3×	`pow1/3`
1×	`distribute-lft-neg-out` `frac-2neg` `distribute-frac-neg` `clear-num` `div-inv`

Counts

4 → 3085

Calls

4 calls:

126.0ms	(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (cbrt 2.0) (cbrt 2.0)) (/ k 2.0))))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series948.0ms

Counts

4 → 6

Calls

4 calls:

948.0ms	(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (cbrt 2.0) (cbrt 2.0)) (/ k 2.0))))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify701.0ms

Algorithm

egg-herbie

Counts

3091 → 3091

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5002	79609

prune12.8s

Filtered

3091 candidates to 2112 candidates (68.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	3089	2	3091
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	3091	6	3097

Merged error: 0b

Counts

3097 → 6

regimes111.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	48	29
2	54	29
3	57	29
4	59	29
5	59	29

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	27257×	body	80	nan
720.0ms	2009×	body	1280	nan
677.0ms	10694×	body	80	valid
452.0ms	1662×	body	640	nan
163.0ms	853×	body	320	nan
48.0ms	416×	body	160	nan