Details

sample173.0ms

Algorithm

intervals

Results

72.0ms	105×	body	1280	valid
19.0ms	50×	body	640	valid
13.0ms	37×	body	10240	exit
11.0ms	161×	body	80	valid
9.0ms	17×	body	1280	nan
9.0ms	187×	body	80	nan
8.0ms	31×	body	320	valid
5.0ms	13×	body	640	nan
2.0ms	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	35	13
3	86	13
4	245	13
5	730	13
6	3688	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize18.0ms

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)))

rewrite178.0ms

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:

9.0ms	(pow x (/ 1.0 n))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
132.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series708.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(pow x (/ 1.0 n))
208.0ms	(pow (+ x 1.0) (/ 1.0 n))
421.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1620	3020
done	5000	2646

prune534.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize13.0ms

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)))

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `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`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

8.0ms	(pow x (/ 1.0 n))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
337.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
123.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow x (/ 1.0 n))
215.0ms	(pow (+ x 1.0) (/ 1.0 n))
408.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
442.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts

249 → 249

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	430	9019
1	825	6371
2	1880	5270
done	5001	4537

prune839.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize16.0ms

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))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

202×	`sqrt-prod`
123×	`*-un-lft-identity`
114×	`add-sqr-sqrt`
110×	`prod-diff`
101×	`unpow-prod-down`
88×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`rem-sqrt-square`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--`

Counts

4 → 236

Calls

4 calls:

4.0ms	(sqrt (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
182.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (pow x (/ 1.0 n)))
206.0ms	(pow (+ x 1.0) (/ 1.0 n))
221.0ms	(pow (+ x 1.0) (/ 1.0 n))
535.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify1.5s

Counts

248 → 248

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	326	9572
1	738	7017
2	1683	5747
done	5000	5090

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

382×	`sqrt-prod`
220×	`prod-diff`
215×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
182×	`unpow-prod-down`
151×	`add-cube-cbrt`
115×	`log-prod`
112×	`exp-sum`
61×	`sqr-pow`
32×	`difference-of-squares`
26×	`pow-unpow`
25×	`distribute-lft-out`
24×	`log-pow`
23×	`exp-prod`
18×	`times-frac`
11×	`fma-neg`
8×	`distribute-lft-out--`
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`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 365

Calls

4 calls:

23.0ms	(pow (+ x 1.0) (/ 1.0 n))
23.0ms	(pow (+ x 1.0) (/ 1.0 n))
247.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
167.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series1.9s

Counts

4 → 12

Calls

4 calls:

226.0ms	(pow (+ x 1.0) (/ 1.0 n))
219.0ms	(pow (+ x 1.0) (/ 1.0 n))
519.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
930.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify3.2s

Counts

377 → 377

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	528	18047
1	905	12556
2	1773	10023
3	4822	8681
done	5000	8681

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.2b

regimes361.0ms

Accuracy

77.2% (2.1b remaining)

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

bsearch2.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	44	137
1	55	137
done	55	137

end0.0ms

sample9.1s

Algorithm

intervals

Results

3.3s	3217×	body	1280	valid
1.5s	1640×	body	640	valid
912.0ms	1170×	body	10240	exit
624.0ms	635×	body	1280	nan
575.0ms	4745×	body	80	valid
435.0ms	5106×	body	80	nan
410.0ms	842×	body	320	valid
404.0ms	654×	body	640	nan
116.0ms	340×	body	320	nan
107.0ms	458×	body	160	valid
35.0ms	178×	body	160	nan