Details

sample268.0ms

Algorithm

intervals

Results

119.0ms	105×	body	1280	valid
31.0ms	50×	body	640	valid
21.0ms	37×	body	10240	exit
16.0ms	161×	body	80	valid
15.0ms	17×	body	1280	nan
13.0ms	187×	body	80	nan
12.0ms	31×	body	320	valid
8.0ms	13×	body	640	nan
3.0ms	9×	body	320	nan
3.0ms	12×	body	160	valid
0.0ms	1×	body	160	nan

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	231	13
5	694	13
6	3452	13
done	5000	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

6.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
133.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series658.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
211.0ms	(pow (+ x 1.0) (/ 1.0 n))
385.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.5s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	190	1337
1	473	1246
2	1191	1206
3	3611	1183
done	5001	1183

prune340.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

6.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
247.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
114.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow x (/ 1.0 n))
238.0ms	(pow (+ x 1.0) (/ 1.0 n))
425.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
349.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.5s

Counts

121 → 121

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	235	1971
1	537	1802
2	1290	1714
3	3771	1683
done	5001	1683

prune583.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
97×	`add-sqr-sqrt`
86×	`pow-unpow`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt`
19×	`unpow-prod-down`
16×	`sqrt-prod`
12×	`difference-of-squares`
11×	`sqr-pow`
8×	`div-inv`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`rem-sqrt-square`
2×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 160

Calls

4 calls:

3.0ms	(sqrt (pow x (/ 1.0 n)))
20.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
119.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (pow x (/ 1.0 n)))
240.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
218.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
538.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify1.4s

Counts

172 → 172

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	266	2793
1	672	2530
2	1721	2482
done	5000	2466

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.3b	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
112×	`add-sqr-sqrt`
86×	`pow-unpow` `*-un-lft-identity`
78×	`add-cube-cbrt`
24×	`difference-of-squares`
22×	`unpow-prod-down`
18×	`sqrt-prod`
17×	`log-pow`
16×	`exp-prod` `sqr-pow`
8×	`div-inv`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 172

Calls

4 calls:

30.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
29.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
238.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
123.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

216.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
204.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
546.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
552.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify3.5s

Counts

184 → 184

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	272	3308
1	654	2990
2	1593	2889
3	4256	2873
done	5000	2873

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

regimes322.0ms

Accuracy

77.3% (2.1b remaining)

Error of 23.1b against oracle of 21.0b and baseline of 30.2b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	142
1	56	142
done	56	142

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.0s	3217×	body	1280	valid
1.3s	1170×	body	10240	exit
959.0ms	1640×	body	640	valid
654.0ms	635×	body	1280	nan
625.0ms	4745×	body	80	valid
508.0ms	654×	body	640	nan
397.0ms	5106×	body	80	nan
354.0ms	842×	body	320	valid
114.0ms	340×	body	320	nan
111.0ms	458×	body	160	valid
34.0ms	178×	body	160	nan