Details

sample138.0ms

Algorithm

intervals

Results

45.0ms	98×	body	1280	valid
22.0ms	31×	body	10240	exit
18.0ms	55×	body	640	valid
8.0ms	150×	body	80	valid
7.0ms	177×	body	80	nan
6.0ms	17×	body	1280	nan
6.0ms	18×	body	640	nan
5.0ms	22×	body	320	valid
2.0ms	12×	body	320	nan
2.0ms	16×	body	160	valid
0.0ms	1×	body	160	nan

simplify2.7s

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	228	13
5	743	13
6	3310	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize8.0ms

Local error

Found 3 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite73.0ms

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))
54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series490.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify874.0ms

Counts

158 → 158

Iterations

Useful iterations: done (868.0ms)

Iter	Nodes	Cost
0	271	4785
1	648	3566
2	1718	3220
done	5000	3079

prune327.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
129×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
100×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 244

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
64.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series744.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow x (/ 1.0 n))
376.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.1s

Counts

256 → 256

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	338	9618
1	780	7177
2	1882	5790
done	5000	5755

prune673.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
1.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

382×	`sqrt-prod`
220×	`prod-diff`
215×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
182×	`unpow-prod-down`
151×	`add-cube-cbrt`
115×	`log-prod`
112×	`exp-sum`
61×	`sqr-pow`
32×	`difference-of-squares`
26×	`pow-unpow`
25×	`distribute-lft-out`
24×	`log-pow`
23×	`exp-prod`
18×	`times-frac`
11×	`fma-neg`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 365

Calls

4 calls:

148.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
68.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

384.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
377.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
154.0ms	(pow (+ x 1.0) (/ 1.0 n))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.0s

Counts

377 → 377

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	528	18047
1	912	12776
2	1829	10023
done	5000	8681

prune952.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
131×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
101×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
15×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 245

Calls

4 calls:

64.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series833.0ms

Counts

4 → 12

Calls

4 calls:

375.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
154.0ms	(pow (+ x 1.0) (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.1s

Counts

257 → 257

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	299	9665
1	663	7220
2	1496	5831
3	4533	5154
done	5001	5132

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.2b

regimes202.0ms

Accuracy

77.4% (2.0b remaining)

Error of 22.6b against oracle of 20.6b and baseline of 29.5b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	99
1	52	99
done	52	99

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3163×	body	1280	valid
556.0ms	1581×	body	640	valid
473.0ms	1160×	body	10240	exit
295.0ms	637×	body	1280	nan
254.0ms	4816×	body	80	valid
225.0ms	680×	body	640	nan
187.0ms	5120×	body	80	nan
179.0ms	795×	body	320	valid
73.0ms	386×	body	320	nan
59.0ms	432×	body	160	valid
19.0ms	162×	body	160	nan