Details

sample234.0ms

Algorithm

intervals

Results

80.0ms	115×	body	1280	valid
28.0ms	36×	body	10240	exit
27.0ms	53×	body	640	valid
16.0ms	23×	body	1280	nan
13.0ms	151×	body	80	valid
11.0ms	20×	body	640	nan
11.0ms	210×	body	80	nan
7.0ms	22×	body	320	valid
4.0ms	14×	body	320	nan
2.0ms	13×	body	160	nan
2.0ms	9×	body	160	valid

simplify3.0s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite155.0ms

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))
127.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
16.0ms	(pow (+ x 1.0) (/ 1.0 n))

series679.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(pow x (/ 1.0 n))
370.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
228.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	190	1337
1	473	1246
2	1192	1206
3	3615	1183
done	5001	1183

prune373.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 21.9b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite230.0ms

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:

7.0ms	(pow x (/ (/ 1.0 n) 2))
153.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
31.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
28.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series953.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow x (/ (/ 1.0 n) 2))
442.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
222.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
194.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify1.1s

Counts

209 → 209

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	297	3215
1	784	2889
2	1989	2839
done	5000	2824

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2)))
1.0b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
99×	`add-sqr-sqrt`
96×	`pow-unpow`
86×	`*-un-lft-identity`
80×	`add-cube-cbrt`
28×	`unpow-prod-down`
15×	`difference-of-squares`
14×	`sqr-pow`
9×	`div-inv`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqrt-prod`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

4.0ms	(pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2)))
90.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
20.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
17.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

428.0ms	(pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2)))
782.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) (sqrt 2))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
234.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
239.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify1.5s

Counts

180 → 180

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	334	4101
1	877	3771
2	2485	3654
done	5001	3644

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.7b

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow (pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cbrt (/ 1.0 n)) (cbrt (sqrt 2)))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.3b	(pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
112×	`add-sqr-sqrt`
106×	`pow-unpow`
92×	`*-un-lft-identity`
86×	`add-cube-cbrt`
45×	`unpow-prod-down`
21×	`difference-of-squares`
19×	`sqr-pow`
13×	`cbrt-prod`
10×	`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 → 184

Calls

4 calls:

126.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow (pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cbrt (/ 1.0 n)) (cbrt (sqrt 2)))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
27.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
31.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (pow (pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cbrt (/ 1.0 n)) (cbrt (sqrt 2)))) (/ (cbrt (/ 1.0 n)) (sqrt 2))))
244.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
202.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
519.0ms	(pow x (/ (cbrt (/ 1.0 n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

simplify2.1s

Counts

196 → 196

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	400	5222
1	1016	4880
2	2724	4733
done	5000	4720

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 21.7b

regimes285.0ms

Accuracy

78.9% (1.8b remaining)

Error of 22.7b against oracle of 20.9b and baseline of 29.4b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	144
1	58	144
done	58	144

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.1s	3162×	body	1280	valid
763.0ms	1550×	body	640	valid
684.0ms	1100×	body	10240	exit
401.0ms	611×	body	1280	nan
360.0ms	4773×	body	80	valid
328.0ms	696×	body	640	nan
272.0ms	5097×	body	80	nan
271.0ms	835×	body	320	valid
102.0ms	358×	body	320	nan
92.0ms	461×	body	160	valid
33.0ms	197×	body	160	nan