Details

sample283.0ms

Algorithm

intervals

Results

72.0ms	91×	body	1280	valid
37.0ms	68×	body	640	valid
35.0ms	34×	body	10240	exit
28.0ms	10×	body	160	nan
20.0ms	32×	body	640	nan
20.0ms	22×	body	1280	nan
16.0ms	166×	body	80	valid
13.0ms	187×	body	80	nan
10.0ms	26×	body	320	valid
5.0ms	14×	body	320	nan
4.0ms	16×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1169
4	263
3	84
2	36
1	19
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize32.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1 n))
0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite120.0ms

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` `insert-posit16` `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 → 82

Calls

3 calls:

6.0ms	(pow x (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
98.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series476.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(pow x (/ 1 n))
121.0ms	(pow (+ x 1) (/ 1 n))
275.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify3.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5007
3	4337
2	1224
1	473
0	176

prune562.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite211.0ms

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` `insert-posit16` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 104

Calls

4 calls:

14.0ms	(pow (+ x 1) (/ 1 n))
71.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
56.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
66.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series955.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(pow (+ x 1) (/ 1 n))
281.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
274.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
260.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	2507
2	827
1	348
0	136

prune767.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
31×	`unpow-prod-down`
30×	`*-un-lft-identity` `difference-of-squares`
20×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `sqrt-prod`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 105

Calls

4 calls:

14.0ms	(pow (+ x 1) (/ 1 n))
51.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
69.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
111.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (+ x 1) (/ 1 n))
212.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
227.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
316.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5004
3	4701
2	1334
1	504
0	196

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))
2.4b	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
33×	`difference-of-squares`
28×	`unpow-prod-down`
25×	`*-un-lft-identity`
21×	`sqr-pow`
18×	`sqrt-prod`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
5×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 106

Calls

4 calls:

14.0ms	(pow (+ x 1) (/ 1 n))
57.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
57.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))
67.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

120.0ms	(pow (+ x 1) (/ 1 n))
267.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
348.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))
370.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

simplify2.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	5004
3	4701
2	1334
1	504
0	196

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.2b

regimes482.0ms

Accuracy

81.3% (1.6b remaining)

Error of 22.6b against oracle of 21.1b and baseline of 29.4b

bsearch2.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	74
1	74
0	58

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.2s	3141×	body	1280	valid
1.4s	1578×	body	640	valid
1.0s	1145×	body	10240	exit
657.0ms	648×	body	1280	nan
498.0ms	4744×	body	80	valid
441.0ms	634×	body	640	nan
391.0ms	5032×	body	80	nan
339.0ms	863×	body	320	valid
129.0ms	368×	body	320	nan
113.0ms	440×	body	160	valid
37.0ms	185×	body	160	nan