Details

sample150.0ms

Algorithm

intervals

Results

49.0ms	101×	body	1280	valid
20.0ms	36×	body	10240	exit
16.0ms	28×	body	1280	nan
14.0ms	40×	body	640	valid
8.0ms	24×	body	640	nan
8.0ms	146×	body	80	valid
7.0ms	32×	body	320	valid
5.0ms	136×	body	80	nan
2.0ms	12×	body	320	nan
2.0ms	15×	body	160	valid
1.0ms	5×	body	160	nan

simplify2.3s

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	215	13
5	726	13
6	3720	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite53.0ms

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

series509.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
288.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
164.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify549.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	190	1337
1	482	1246
2	1564	1206
done	5001	1206

prune263.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

43.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
2.0ms	(pow x (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series822.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
63.0ms	(pow x (/ 1.0 n))
303.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.1s

Counts

138 → 138

Iterations

Useful iterations: 2 (447.0ms)

Iter	Nodes	Cost
0	261	2940
1	699	2513
2	2336	2414
done	5000	2414

prune437.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

45.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
2.0ms	(pow x (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series802.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
57.0ms	(pow x (/ 1.0 n))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
175.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify982.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (262.0ms)

Iter	Nodes	Cost
0	261	2940
1	699	2513
2	2336	2414
done	5000	2414

prune494.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

46.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
2.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series880.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
62.0ms	(pow x (/ 1.0 n))
313.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
176.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify923.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (235.0ms)

Iter	Nodes	Cost
0	261	2940
1	699	2513
2	2336	2414
done	5000	2414

prune548.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.8b

regimes252.0ms

Accuracy

83.5% (1.4b remaining)

Error of 22.3b against oracle of 20.8b and baseline of 29.4b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	97
1	51	97
2	55	97
3	58	97
done	58	97

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	3138×	body	1280	valid
555.0ms	1574×	body	640	valid
479.0ms	1147×	body	10240	exit
293.0ms	618×	body	1280	nan
264.0ms	4726×	body	80	valid
231.0ms	669×	body	640	nan
203.0ms	885×	body	320	valid
192.0ms	5002×	body	80	nan
65.0ms	449×	body	160	valid
65.0ms	327×	body	320	nan
20.0ms	170×	body	160	nan