Details

sample145.0ms

Algorithm

intervals

Results

46.0ms	98×	body	1280	valid
22.0ms	31×	body	10240	exit
21.0ms	55×	body	640	valid
8.0ms	150×	body	80	valid
7.0ms	177×	body	80	nan
7.0ms	17×	body	1280	nan
6.0ms	18×	body	640	nan
5.0ms	22×	body	320	valid
2.0ms	12×	body	320	nan
2.0ms	16×	body	160	valid
0.0ms	1×	body	160	nan

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	224	13
5	687	13
6	3245	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize9.0ms

Local error

Found 3 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite67.0ms

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:

2.0ms	(pow x (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series501.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
166.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify873.0ms

Counts

158 → 158

Iterations

Useful iterations: done (681.0ms)

Iter	Nodes	Cost
0	271	4785
1	626	3566
2	1690	3020
done	5000	2999

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ (/ 1.0 n) 2))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
119×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
84×	`times-frac`
83×	`unpow-prod-down`
77×	`prod-diff`
73×	`sqrt-prod`
69×	`pow-unpow`
29×	`sqr-pow`
12×	`difference-of-squares`
11×	`fma-neg`
10×	`distribute-lft-out`
7×	`pow1` `add-exp-log`
6×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 234

Calls

4 calls:

5.0ms	(pow x (/ (/ 1.0 n) 2))
59.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series768.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow x (/ (/ 1.0 n) 2))
400.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify979.0ms

Counts

246 → 246

Iterations

Useful iterations: done (970.0ms)

Iter	Nodes	Cost
0	382	8156
1	944	6063
2	2501	5027
done	5000	4950

prune793.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize22.0ms

Local error

Found 4 expressions with local error:

2.1b	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

154×	`prod-diff`
149×	`*-un-lft-identity`
148×	`unpow-prod-down`
145×	`add-sqr-sqrt`
138×	`sqrt-prod`
111×	`add-cube-cbrt`
82×	`log-prod`
79×	`exp-sum`
53×	`sqr-pow`
26×	`pow-unpow`
24×	`difference-of-squares`
18×	`times-frac`
17×	`log-pow` `distribute-lft-out`
16×	`exp-prod`
11×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `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` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 285

Calls

4 calls:

120.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))
58.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

412.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))
408.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify934.0ms

Counts

297 → 297

Iterations

Useful iterations: done (915.0ms)

Iter	Nodes	Cost
0	451	14224
1	780	9934
2	1683	7868
done	5000	6430

prune821.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.2b

localize22.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(pow (+ x 1.0) (/ 1.0 n))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
84×	`unpow-prod-down`
77×	`prod-diff`
74×	`add-cube-cbrt`
73×	`sqrt-prod`
39×	`pow-unpow`
29×	`sqr-pow`
27×	`times-frac`
12×	`difference-of-squares`
11×	`fma-neg` `distribute-lft-out`
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` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 205

Calls

4 calls:

57.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series880.0ms

Counts

4 → 12

Calls

4 calls:

416.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
158.0ms	(pow (+ x 1.0) (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
157.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.9s

Counts

217 → 217

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	266	7787
1	575	5751
2	1411	4706
3	4774	3978
done	5000	3978

prune936.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.2b

regimes206.0ms

Accuracy

77.4% (2.0b remaining)

Error of 22.6b against oracle of 20.6b and baseline of 29.5b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	101
1	53	101
done	53	101

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	3163×	body	1280	valid
572.0ms	1581×	body	640	valid
503.0ms	1160×	body	10240	exit
320.0ms	637×	body	1280	nan
275.0ms	4816×	body	80	valid
247.0ms	680×	body	640	nan
203.0ms	5120×	body	80	nan
189.0ms	795×	body	320	valid
79.0ms	386×	body	320	nan
63.0ms	432×	body	160	valid
20.0ms	162×	body	160	nan