Details

sample157.0ms

Algorithm

intervals

Results

58.0ms	110×	body	1280	valid
21.0ms	56×	body	640	valid
13.0ms	20×	body	1280	nan
13.0ms	37×	body	10240	exit
8.0ms	131×	body	80	valid
8.0ms	21×	body	640	nan
5.0ms	22×	body	320	valid
5.0ms	110×	body	80	nan
3.0ms	13×	body	320	nan
2.0ms	11×	body	160	valid

simplify32.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize43.0ms

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)))

rewrite103.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
85.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series532.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(pow x (/ 1.0 n))
155.0ms	(pow (+ x 1.0) (/ 1.0 n))
310.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify41.0ms

Counts: 88 → 88

prune284.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize16.0ms

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)))

rewrite140.0ms

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:

8.0ms	(pow x (/ (/ 1.0 n) 2))
16.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
91.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow x (/ (/ 1.0 n) 2))
165.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
165.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
319.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify70.0ms

Counts: 209 → 209

prune905.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

localize21.0ms

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)))

rewrite267.0ms

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))
84.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
86.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
82.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

174.0ms	(pow (+ x 1.0) (/ 1.0 n))
312.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
334.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
315.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Counts: 112 → 112

prune512.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
32×	`*-un-lft-identity`
24×	`sqr-pow`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

79.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
81.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
81.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
79.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

324.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
315.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
312.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
309.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify80.0ms

Counts: 108 → 108

prune546.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

regimes257.0ms

Accuracy

85.7% (1.2b remaining)

Error of 21.7b against oracle of 20.5b and baseline of 29.2b

bsearch1.0ms

simplify1.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	3165×	body	1280	valid
631.0ms	1156×	body	10240	exit
618.0ms	1531×	body	640	valid
593.0ms	691×	body	1280	nan
358.0ms	4619×	body	80	valid
256.0ms	860×	body	320	valid
253.0ms	620×	body	640	nan
225.0ms	5017×	body	80	nan
76.0ms	337×	body	320	nan
69.0ms	424×	body	160	valid
23.0ms	179×	body	160	nan