Details

sample143.0ms

Algorithm

intervals

Results

53.0ms	113×	body	1280	valid
17.0ms	31×	body	10240	exit
16.0ms	45×	body	640	valid
13.0ms	24×	body	1280	nan
8.0ms	151×	body	80	valid
5.0ms	25×	body	320	valid
5.0ms	21×	body	640	nan
5.0ms	134×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	11×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	209	13
5	656	13
6	3056	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series460.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
263.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (636.0ms)

Iter	Nodes	Cost
0	190	1337
1	478	1246
2	1258	1206
3	3924	1183
done	5000	1183

prune240.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
4.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`times-frac`
11×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ 1.0 n))
59.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify1.5s

Counts

109 → 109

Iterations

Useful iterations: 3 (694.0ms)

Iter	Nodes	Cost
0	181	1579
1	467	1298
2	1279	1256
3	4183	1221
done	5001	1221

prune337.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
96.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify1.6s

Counts

121 → 121

Iterations

Useful iterations: 3 (877.0ms)

Iter	Nodes	Cost
0	235	1971
1	543	1802
2	1359	1714
3	4075	1683
done	5001	1683

prune352.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.8b

localize17.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
37.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
446.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
435.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify952.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (269.0ms)

Iter	Nodes	Cost
0	141	2446
1	301	2374
2	751	2196
3	2288	2148
done	5000	2148

prune428.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.7b

regimes266.0ms

Accuracy

82.2% (1.5b remaining)

Error of 21.9b against oracle of 20.4b and baseline of 29.0b

bsearch181.0ms

Steps

Iters	Range		Point
10	0.11513722063736925	8521518135.486671	196016184.31866574
8	-2.2021465089483198e+21	-7.884632933156152e+16	-8.092517375237888e+16

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	75
1	41	53
done	41	53

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3210×	body	1280	valid
561.0ms	1581×	body	640	valid
444.0ms	1119×	body	10240	exit
316.0ms	660×	body	1280	nan
247.0ms	4726×	body	80	valid
215.0ms	676×	body	640	nan
197.0ms	848×	body	320	valid
192.0ms	4956×	body	80	nan
69.0ms	341×	body	320	nan
61.0ms	438×	body	160	valid
25.0ms	191×	body	160	nan