Details

sample221.0ms

Algorithm

intervals

Results

62.0ms	130×	body	1280	valid
38.0ms	62×	body	1280	nan
24.0ms	57×	body	640	nan
23.0ms	54×	body	640	valid
19.0ms	44×	body	5120	exit
10.0ms	40×	body	320	valid
9.0ms	191×	body	80	nan
8.0ms	30×	body	320	nan
5.0ms	94×	body	80	valid
2.0ms	14×	body	160	valid
2.0ms	10×	body	160	nan

simplify36.0ms

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

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: 31.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite31.0ms

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:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series479.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify69.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

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

prune270.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	5	159

Merged error: 20.6b

Counts

159 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
177×	`*-un-lft-identity`
168×	`prod-diff`
149×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
72×	`sqr-pow`
36×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`fma-neg`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 297

Calls

4 calls:

9.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

578.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify92.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	554	5996
1	1534	4421
2	5001	4401

prune624.0ms

Filtered

309 candidates to 157 candidates (50.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	309	5	314

Merged error: 20.6b

Counts

314 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
151×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
72×	`sqr-pow`
36×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`fma-neg`
19×	`log-pow`
18×	`exp-prod`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `log-prod` `flip3--` `diff-log` `flip--`
1×	`rem-log-exp`

Counts

4 → 302

Calls

4 calls:

11.0ms	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

594.0ms	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
293.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	589	5920
1	1582	4331
2	5001	4311

prune733.0ms

Filtered

314 candidates to 160 candidates (51.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	312	2	314
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	313	6	319

Merged error: 20.6b

Counts

319 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

264×	`unpow-prod-down`
224×	`*-un-lft-identity` `prod-diff`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
88×	`sqr-pow`
36×	`distribute-lft-out` `difference-of-squares`
32×	`fma-neg`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 360

Calls

4 calls:

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

series1.3s

Counts

4 → 12

Calls

4 calls:

281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
482.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify109.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	413	7360
1	1182	5280
2	5002	5264

prune918.0ms

Filtered

372 candidates to 176 candidates (47.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	370	2	372
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	372	6	378

Merged error: 20.6b

Counts

378 → 6

regimes231.0ms

Accuracy

82.8% (1.8b remaining)

Error of 24.0b against oracle of 22.2b and baseline of 32.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	112
1	69	112

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.0s	3885×	body	1280	valid
1.3s	2078×	body	1280	nan
746.0ms	1719×	body	640	nan
688.0ms	1406×	body	5120	exit
654.0ms	1782×	body	640	valid
295.0ms	6036×	body	80	nan
246.0ms	911×	body	320	nan
222.0ms	917×	body	320	valid
169.0ms	3082×	body	80	valid
70.0ms	448×	body	160	nan
69.0ms	443×	body	160	valid