Details

sample219.0ms

Algorithm

intervals

Results

88.0ms	105×	body	1280	valid
24.0ms	50×	body	640	valid
18.0ms	37×	body	10240	exit
13.0ms	161×	body	80	valid
13.0ms	17×	body	1280	nan
11.0ms	31×	body	320	valid
10.0ms	187×	body	80	nan
6.0ms	13×	body	640	nan
3.0ms	9×	body	320	nan
2.0ms	12×	body	160	valid
0.0ms	1×	body	160	nan

simplify3.3s

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: 31.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite118.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
100.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series680.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(pow x (/ 1.0 n))
209.0ms	(pow (+ x 1.0) (/ 1.0 n))
376.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.6s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	190	1337
1	473	1246
2	1191	1206
3	3611	1183
done	5001	1183

prune413.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite415.0ms

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:

5.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
269.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
117.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow x (/ 1.0 n))
178.0ms	(pow (+ x 1.0) (/ 1.0 n))
393.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
413.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.7s

Counts

121 → 121

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	235	1971
1	537	1802
2	1290	1714
3	3771	1683
done	5001	1683

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
97×	`add-sqr-sqrt`
86×	`pow-unpow`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt`
19×	`unpow-prod-down`
16×	`sqrt-prod`
12×	`difference-of-squares`
11×	`sqr-pow`
8×	`div-inv`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`rem-sqrt-square`
2×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 160

Calls

4 calls:

3.0ms	(sqrt (pow x (/ 1.0 n)))
23.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
16.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
154.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (pow x (/ 1.0 n)))
204.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
208.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
573.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify1.5s

Counts

172 → 172

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	266	2793
1	672	2530
2	1721	2482
done	5000	2466

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.3b	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
2.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
112×	`add-sqr-sqrt`
86×	`pow-unpow` `*-un-lft-identity`
78×	`add-cube-cbrt`
24×	`difference-of-squares`
22×	`unpow-prod-down`
18×	`sqrt-prod`
17×	`log-pow`
16×	`exp-prod` `sqr-pow`
8×	`div-inv`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 172

Calls

4 calls:

23.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
288.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
139.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

254.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
229.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
497.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))
475.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify3.7s

Counts

184 → 184

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	272	3308
1	654	2990
2	1593	2889
3	4256	2873
done	5000	2873

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

regimes291.0ms

Accuracy

77.3% (2.1b remaining)

Error of 23.1b against oracle of 21.0b and baseline of 30.2b

bsearch2.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	142
1	56	142
done	56	142

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.7s	3217×	body	1280	valid
1.3s	1170×	body	10240	exit
934.0ms	1640×	body	640	valid
839.0ms	5106×	body	80	nan
531.0ms	4745×	body	80	valid
523.0ms	635×	body	1280	nan
362.0ms	654×	body	640	nan
346.0ms	842×	body	320	valid
108.0ms	340×	body	320	nan
97.0ms	458×	body	160	valid
33.0ms	178×	body	160	nan