Details

sample224.0ms

Algorithm

intervals

Results

79.0ms	105×	body	1280	valid
29.0ms	50×	body	640	valid
20.0ms	37×	body	10240	exit
15.0ms	161×	body	80	valid
14.0ms	17×	body	1280	nan
11.0ms	187×	body	80	nan
10.0ms	31×	body	320	valid
8.0ms	13×	body	640	nan
3.0ms	12×	body	160	valid
3.0ms	9×	body	320	nan
0.0ms	1×	body	160	nan

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	245	13
5	730	13
6	3688	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize19.0ms

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)))

rewrite168.0ms

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:

4.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
137.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series672.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(pow x (/ 1.0 n))
208.0ms	(pow (+ x 1.0) (/ 1.0 n))
385.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

158 → 158

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1620	3020
done	5000	2646

prune535.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize25.0ms

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)))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `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 → 237

Calls

4 calls:

9.0ms	(pow x (/ 1.0 n))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
233.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
171.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

114.0ms	(pow x (/ 1.0 n))
237.0ms	(pow (+ x 1.0) (/ 1.0 n))
418.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
368.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.7s

Counts

249 → 249

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	430	9019
1	825	6371
2	1880	5270
done	5001	4537

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ (/ 1.0 n) 2))
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)) (pow x (/ (/ 1.0 n) 2)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

16.0ms	(pow x (/ (/ 1.0 n) 2))
21.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
17.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
133.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow x (/ (/ 1.0 n) 2))
268.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
214.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
455.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify1.8s

Counts

281 → 281

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	378	7611
1	958	5824
2	2415	5145
done	5000	4547

prune1.5s

Pruning

9 alts after pruning (9 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)) (pow x (/ (/ 1.0 n) 2)))))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

188×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
136×	`unpow-prod-down`
132×	`times-frac`
112×	`prod-diff`
86×	`pow-unpow`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg` `div-inv`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 298

Calls

4 calls:

25.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
250.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
166.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

234.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
231.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
417.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
415.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify1.9s

Counts

310 → 310

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	469	12142
1	945	8666
2	2205	7299
done	5000	6111

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.2b

regimes303.0ms

Accuracy

77.3% (2.1b remaining)

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

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	147
1	56	147
done	56	147

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	3217×	body	1280	valid
967.0ms	1170×	body	10240	exit
956.0ms	1640×	body	640	valid
753.0ms	4745×	body	80	valid
731.0ms	842×	body	320	valid
532.0ms	635×	body	1280	nan
434.0ms	654×	body	640	nan
376.0ms	5106×	body	80	nan
108.0ms	340×	body	320	nan
101.0ms	458×	body	160	valid
32.0ms	178×	body	160	nan