Details

sample219.0ms

Algorithm

intervals

Results

59.0ms	113×	body	1280	valid
46.0ms	41×	body	1280	nan
24.0ms	58×	body	640	valid
21.0ms	33×	body	640	nan
18.0ms	116×	body	80	overflowed
10.0ms	104×	body	80	valid
8.0ms	176×	body	80	nan
7.0ms	24×	body	320	valid
4.0ms	21×	body	160	valid
2.0ms	5×	body	320	nan
1.0ms	5×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

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: 30.6b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

9.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series276.0ms

Counts

1 → 3

Calls

1 calls:

276.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify75.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune88.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	22	5	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	5	28

Merged error: 20.4b

Counts

28 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
33×	`*-un-lft-identity`
24×	`sqr-pow`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 97

Calls

4 calls:

9.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

568.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify120.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	362	1439
1	973	1385
2	4399	1363
3	5002	1363

prune574.0ms

Filtered

109 candidates to 93 candidates (85.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Merged error: 20.4b

Counts

114 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (- 0.5) (* (pow x 2) n))
1.1b	(/ (log (/ 1 x)) (pow n 2))
3.0b	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
7.3b	(* (pow x 2) n)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
94×	`times-frac`
59×	`*-un-lft-identity`
44×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`unpow-prod-down` `log-pow`
25×	`pow1` `associate-r`
21×	`associate-l`
18×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`difference-of-squares`
12×	`unpow2` `sqr-pow`
9×	`pow-flip` `associate-/r*` `inv-pow`
8×	`div-exp` `prod-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `unswap-sqr`
4×	`cbrt-undiv` `div-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `add-log-exp`
3×	`distribute-rgt-in` `frac-times` `pow-to-exp` `log-div` `distribute-lft-in` `associate-*r/` `pow-exp`
2×	`neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `distribute-frac-neg` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`neg-sub0` `log-rec` `pow-prod-down` `associate-*l/`

Counts

4 → 207

Calls

4 calls:

6.0ms	(/ (- 0.5) (* (pow x 2) n))
7.0ms	(/ (log (/ 1 x)) (pow n 2))
45.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
5.0ms	(* (pow x 2) n)

series230.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- 0.5) (* (pow x 2) n))
61.0ms	(/ (log (/ 1 x)) (pow n 2))
126.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
17.0ms	(* (pow x 2) n)

simplify113.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	892	1593
1	4324	1425
2	5003	1420

prune579.0ms

Filtered

219 candidates to 147 candidates (67.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	212	7	219
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	213	11	224

Merged error: 20.2b

Counts

224 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (log x) (pow n 2))
2.5b	(+ (/ (/ 1.0 x) n) (* (/ 1.0 x) (/ (log x) (pow n 2))))
7.3b	(* (pow x 2) n)
7.9b	(* (/ 1.0 x) (/ (log x) (pow n 2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac`
85×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
38×	`add-exp-log`
33×	`unpow-prod-down`
23×	`pow1`
21×	`associate-l`
20×	`add-cbrt-cube`
17×	`log-pow`
14×	`unswap-sqr`
13×	`div-exp` `unpow2` `sqr-pow`
11×	`prod-exp`
8×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`pow-to-exp` `pow-exp` `div-inv` `associate-/l*`
3×	`frac-add`
2×	`frac-times` `associate-r/` `associate-l/` `*-commutative`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 183

Calls

4 calls:

5.0ms	(/ (log x) (pow n 2))
13.0ms	(+ (/ (/ 1.0 x) n) (* (/ 1.0 x) (/ (log x) (pow n 2))))
5.0ms	(* (pow x 2) n)
18.0ms	(* (/ 1.0 x) (/ (log x) (pow n 2)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (log x) (pow n 2))
146.0ms	(+ (/ (/ 1.0 x) n) (* (/ 1.0 x) (/ (log x) (pow n 2))))
17.0ms	(* (pow x 2) n)
84.0ms	(* (/ 1.0 x) (/ (log x) (pow n 2)))

simplify96.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	790	1367
1	3898	1179
2	5001	1176

prune454.0ms

Filtered

195 candidates to 123 candidates (63.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	194	12	206

Merged error: 20.2b

Counts

206 → 12

regimes296.0ms

Accuracy

79.2% (2.3b remaining)

Error of 23.8b against oracle of 21.5b and baseline of 32.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	55
1	55	55

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.1s	3915×	body	1280	valid
1.2s	1146×	body	1280	nan
754.0ms	1743×	body	640	valid
646.0ms	934×	body	640	nan
564.0ms	4016×	body	80	overflowed
327.0ms	6364×	body	80	nan
317.0ms	3207×	body	80	valid
281.0ms	933×	body	320	valid
182.0ms	466×	body	320	nan
83.0ms	446×	body	160	valid
44.0ms	210×	body	160	nan