Details

sample202.0ms

Algorithm

intervals

Results

54.0ms	123×	body	1280	valid
38.0ms	66×	body	1280	nan
20.0ms	53×	body	640	nan
18.0ms	57×	body	640	valid
15.0ms	54×	body	10240	exit
9.0ms	102×	body	80	valid
8.0ms	34×	body	320	nan
7.0ms	180×	body	80	nan
7.0ms	34×	body	320	valid
3.0ms	22×	body	160	valid
2.0ms	15×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series491.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(pow (+ x 1.0) (/ 1.0 n))
57.0ms	(pow x (/ 1.0 n))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune345.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.1b	(pow x (/ (/ 1.0 n) 2))
0.1b	(pow x (/ (/ 1.0 n) 2))
3.6b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
169×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
76×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 268

Calls

4 calls:

12.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
7.0ms	(pow x (/ (/ 1.0 n) 2))
7.0ms	(pow x (/ (/ 1.0 n) 2))
11.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
56.0ms	(pow x (/ (/ 1.0 n) 2))
62.0ms	(pow x (/ (/ 1.0 n) 2))
278.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify90.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	985	3476
1	3500	2809
2	5001	2805

prune907.0ms

Filtered

280 candidates to 203 candidates (72.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
66×	`unpow-prod-down`
57×	`add-cube-cbrt`
56×	`prod-diff`
39×	`cbrt-prod`
27×	`times-frac`
22×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 162

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
12.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series886.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (/ 1.0 n))
198.0ms	(cbrt (/ 1.0 n))
204.0ms	(cbrt (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	502	2713
1	1420	2044
2	5001	2028

prune631.0ms

Filtered

174 candidates to 110 candidates (63.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
3.9b	(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ (/ (/ 1.0 n) 2) 2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
77×	`prod-diff`
73×	`sqrt-prod`
72×	`unpow-prod-down`
71×	`add-cube-cbrt`
39×	`cbrt-prod`
27×	`times-frac`
26×	`sqr-pow`
12×	`difference-of-squares`
11×	`fma-neg`
8×	`distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 187

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
14.0ms	(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ (/ (/ 1.0 n) 2) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (/ 1.0 n))
204.0ms	(cbrt (/ 1.0 n))
200.0ms	(cbrt (/ 1.0 n))
407.0ms	(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ (/ (/ 1.0 n) 2) 2)))

simplify71.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	548	4138
1	1464	2969
2	5001	2916

prune768.0ms

Filtered

199 candidates to 117 candidates (58.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.1b

regimes211.0ms

Accuracy

79.8% (2.2b remaining)

Error of 24.5b against oracle of 22.4b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	117
1	73	117

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.0s	3883×	body	1280	valid
1.3s	2258×	body	1280	nan
756.0ms	1889×	body	640	nan
617.0ms	1829×	body	640	valid
590.0ms	1394×	body	10240	exit
270.0ms	6193×	body	80	nan
218.0ms	909×	body	320	nan
201.0ms	904×	body	320	valid
152.0ms	3121×	body	80	valid
66.0ms	468×	body	160	nan
60.0ms	436×	body	160	valid