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
7.0ms	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

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	209	13
5	656	13
6	3056	13
done	5001	13

prune2.0ms

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))

rewrite48.0ms

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:

2.0ms	(pow x (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))

series657.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
449.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (637.0ms)

Iter	Nodes	Cost
0	190	1337
1	478	1246
2	1258	1206
3	3930	1183
done	5001	1183

prune227.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
101×	`add-sqr-sqrt`
99×	`pow-unpow`
90×	`*-un-lft-identity`
84×	`add-cube-cbrt`
18×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`sqr-pow`
9×	`sqrt-prod` `div-inv`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
10.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series674.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow x (/ 1.0 n))
330.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
143.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
141.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify787.0ms

Counts

180 → 180

Iterations

Useful iterations: done (782.0ms)

Iter	Nodes	Cost
0	277	2841
1	758	2581
2	2037	2527
done	5000	2526

prune672.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
1.8b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite163.0ms

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:

95.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
43.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series981.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
337.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
150.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
145.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify2.1s

Counts

184 → 184

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	272	3308
1	669	2990
2	1705	2889
3	4903	2873
done	5000	2873

prune771.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
129×	`add-sqr-sqrt` `pow-unpow`
120×	`*-un-lft-identity`
112×	`add-cube-cbrt`
19×	`unpow-prod-down`
12×	`div-inv` `difference-of-squares`
10×	`sqr-pow`
9×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 199

Calls

4 calls:

44.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series787.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
149.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
144.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
152.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify2.1s

Counts

211 → 211

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	229	3360
1	606	3037
2	1609	2987
3	4770	2973
done	5000	2973

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 21.2b

regimes180.0ms

Accuracy

77.6% (2.0b remaining)

Error of 22.6b against oracle of 20.7b and baseline of 29.5b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	101
1	53	101
done	53	101

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3163×	body	1280	valid
552.0ms	1581×	body	640	valid
474.0ms	1160×	body	10240	exit
301.0ms	637×	body	1280	nan
257.0ms	4816×	body	80	valid
227.0ms	680×	body	640	nan
189.0ms	5120×	body	80	nan
182.0ms	795×	body	320	valid
73.0ms	386×	body	320	nan
62.0ms	432×	body	160	valid
19.0ms	162×	body	160	nan