Details

sample128.0ms

Algorithm

intervals

Results

45.0ms	95×	body	1280	valid
20.0ms	57×	body	640	valid
8.0ms	18×	body	1280	nan
8.0ms	150×	body	80	valid
8.0ms	29×	body	10240	exit
6.0ms	15×	body	640	nan
6.0ms	158×	body	80	nan
5.0ms	22×	body	320	valid
3.0ms	17×	body	320	nan
3.0ms	19×	body	160	valid
1.0ms	7×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	224	13
5	687	13
6	3439	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite63.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series497.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify740.0ms

Counts

158 → 158

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	271	4785
1	626	3566
2	1852	3220
done	5000	3172

prune337.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.9b	(pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

152×	`unpow-prod-down`
91×	`*-un-lft-identity`
88×	`prod-diff`
82×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
41×	`sqr-pow`
18×	`pow-unpow`
15×	`difference-of-squares`
13×	`distribute-lft-out`
10×	`times-frac`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

0.0ms	(cbrt n)
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
2.0ms	(pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt n)
155.0ms	(pow (+ x 1.0) (/ 1.0 n))
282.0ms	(pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
583.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

simplify1.2s

Counts

202 → 202

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	359	15315
1	784	10443
2	2554	8028
done	5000	8004

prune612.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 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)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
277.0ms	(- (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)))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify659.0ms

Counts

312 → 312

Iterations

Useful iterations: done (646.0ms)

Iter	Nodes	Cost
0	234	12646
1	514	9161
2	1462	8133
done	5001	7989

prune737.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 24.9b

localize16.0ms

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

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 358

Calls

4 calls:

46.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
97.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

286.0ms	(- (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)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
283.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify668.0ms

Counts

370 → 370

Iterations

Useful iterations: done (651.0ms)

Iter	Nodes	Cost
0	344	16510
1	563	11634
2	1320	9453
done	5001	8441

prune902.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 24.9b

regimes260.0ms

Accuracy

80.8% (1.6b remaining)

Error of 22.6b against oracle of 21.0b and baseline of 29.4b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	107
1	47	107
done	47	107

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3161×	body	1280	valid
542.0ms	1557×	body	640	valid
428.0ms	1094×	body	10240	exit
310.0ms	654×	body	1280	nan
246.0ms	4668×	body	80	valid
201.0ms	615×	body	640	nan
182.0ms	807×	body	320	valid
181.0ms	4983×	body	80	nan
63.0ms	331×	body	320	nan
62.0ms	454×	body	160	valid
20.0ms	183×	body	160	nan