Details

sample226.0ms

Algorithm

intervals

Results

73.0ms	110×	body	1280	valid
45.0ms	131×	body	80	valid
25.0ms	56×	body	640	valid
16.0ms	20×	body	1280	nan
14.0ms	37×	body	10240	exit
10.0ms	21×	body	640	nan
6.0ms	110×	body	80	nan
6.0ms	22×	body	320	valid
4.0ms	13×	body	320	nan
2.0ms	11×	body	160	valid

simplify3.4s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite137.0ms

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:

8.0ms	(pow x (/ 1.0 n))
21.0ms	(pow (+ x 1.0) (/ 1.0 n))
104.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series667.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(pow x (/ 1.0 n))
181.0ms	(pow (+ x 1.0) (/ 1.0 n))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.6s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.1s)

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

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ (/ 1.0 n) 2))
0.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 197

Calls

4 calls:

15.0ms	(pow x (/ (/ 1.0 n) 2))
30.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
32.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
143.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow x (/ (/ 1.0 n) 2))
252.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
222.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
430.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify1.5s

Counts

209 → 209

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	297	3215
1	784	2889
2	1990	2839
done	5000	2824

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

21.0ms	(pow (+ x 1.0) (/ 1.0 n))
110.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
126.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
136.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

190.0ms	(pow (+ x 1.0) (/ 1.0 n))
449.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
483.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
348.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	149	2370
1	358	2257
2	892	2151
3	2475	2130
done	5001	2114

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
156.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
136.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
169.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

205.0ms	(pow (+ x 1.0) (/ 1.0 n))
417.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
445.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
361.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	149	2370
1	358	2257
2	892	2151
3	2475	2130
done	5001	2114

prune762.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.5b

regimes380.0ms

Accuracy

85.3% (1.3b remaining)

Error of 21.8b against oracle of 20.5b and baseline of 29.2b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	107
1	45	107
done	45	107

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.1s	3165×	body	1280	valid
1.3s	1531×	body	640	valid
991.0ms	1156×	body	10240	exit
609.0ms	691×	body	1280	nan
415.0ms	860×	body	320	valid
415.0ms	620×	body	640	nan
403.0ms	4619×	body	80	valid
388.0ms	5017×	body	80	nan
111.0ms	337×	body	320	nan
96.0ms	424×	body	160	valid
34.0ms	179×	body	160	nan