Details

sample132.0ms

Algorithm

intervals

Results

45.0ms	95×	body	1280	valid
20.0ms	57×	body	640	valid
9.0ms	158×	body	80	nan
8.0ms	18×	body	1280	nan
8.0ms	150×	body	80	valid
8.0ms	29×	body	10240	exit
6.0ms	15×	body	640	nan
5.0ms	22×	body	320	valid
3.0ms	17×	body	320	nan
3.0ms	19×	body	160	valid
1.0ms	7×	body	160	nan

simplify1.7s

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	3058	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite55.0ms

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))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series499.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: 3 (598.0ms)

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

prune256.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.9b	(pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
24×	`unpow-prod-down`
23×	`pow-unpow`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac` `difference-of-squares`
13×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`cbrt-prod` `sqrt-prod`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 91

Calls

4 calls:

0.0ms	(cbrt n)
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
2.0ms	(pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt n)
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
224.0ms	(pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
510.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))))

simplify632.0ms

Counts

103 → 103

Iterations

Useful iterations: done (629.0ms)

Iter	Nodes	Cost
0	270	2321
1	661	2200
2	2008	1963
done	5000	1961

prune415.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
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	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite136.0ms

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

Counts

4 → 100

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
296.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.2s

Counts

112 → 112

Iterations

Useful iterations: 3 (433.0ms)

Iter	Nodes	Cost
0	149	2370
1	361	2257
2	913	2151
3	2604	2130
done	5000	2130

prune421.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 24.1b

localize19.0ms

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	(- (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)))))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
34×	`*-un-lft-identity`
24×	`sqr-pow`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 102

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)))
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)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify656.0ms

Counts

114 → 114

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	141	2650
1	291	2494
2	672	2344
3	1874	2320
done	5001	2320

prune480.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

regimes283.0ms

Accuracy

80.2% (1.7b remaining)

Error of 22.3b against oracle of 20.6b and baseline of 29.4b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	103
1	48	103
done	48	103

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3161×	body	1280	valid
540.0ms	1557×	body	640	valid
439.0ms	1094×	body	10240	exit
330.0ms	654×	body	1280	nan
258.0ms	4668×	body	80	valid
210.0ms	615×	body	640	nan
187.0ms	4983×	body	80	nan
180.0ms	807×	body	320	valid
65.0ms	331×	body	320	nan
64.0ms	454×	body	160	valid
21.0ms	183×	body	160	nan