Details

sample208.0ms

Algorithm

intervals

Results

63.0ms	84×	body	1280	valid
29.0ms	53×	body	640	valid
17.0ms	21×	body	1280	nan
14.0ms	28×	body	10240	exit
13.0ms	41×	body	320	valid
13.0ms	144×	body	80	valid
11.0ms	176×	body	80	nan
10.0ms	22×	body	640	nan
4.0ms	13×	body	320	nan
4.0ms	18×	body	160	valid
1.0ms	4×	body	160	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1264
4	252
3	86
2	35
1	17
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize30.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite145.0ms

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:

4.0ms	(pow x (/ 1.0 n))
13.0ms	(pow (+ x 1.0) (/ 1.0 n))
120.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series695.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(pow x (/ 1.0 n))
191.0ms	(pow (+ x 1.0) (/ 1.0 n))
428.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.1s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune850.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.3b

localize91.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

18.0ms	(pow (+ x 1.0) (/ 1.0 n))
109.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
101.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
125.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

212.0ms	(pow (+ x 1.0) (/ 1.0 n))
438.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
376.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
363.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.1s

Counts

312 → 312

Iterations

Iter	Nodes
done	5000
2	2187
1	601
0	233

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.3b

localize80.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
189×	`prod-diff`
188×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
73×	`sqrt-prod`
71×	`sqr-pow`
30×	`difference-of-squares`
27×	`fma-neg` `distribute-lft-out`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 325

Calls

4 calls:

8.0ms	(pow (+ x 1.0) (/ 1.0 n))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
116.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

263.0ms	(pow (+ x 1.0) (/ 1.0 n))
382.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
605.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify2.4s

Counts

337 → 337

Iterations

Iter	Nodes
done	5000
2	3586
1	980
0	395

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.3b

localize85.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (sqrt (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (sqrt (pow x (/ (/ 1.0 n) 2))))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

352×	`sqrt-prod`
252×	`prod-diff`
236×	`*-un-lft-identity`
231×	`unpow-prod-down`
217×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
79×	`sqr-pow`
38×	`difference-of-squares`
30×	`fma-neg` `distribute-lft-out`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
8×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 400

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
118.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
101.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
92.0ms	(- (sqrt (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (sqrt (pow x (/ (/ 1.0 n) 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

226.0ms	(pow (+ x 1.0) (/ 1.0 n))
375.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
382.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
478.0ms	(- (sqrt (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (sqrt (pow x (/ (/ 1.0 n) 2))))

simplify2.6s

Counts

412 → 412

Iterations

Iter	Nodes
done	5000
2	3651
1	1107
0	469

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.3b

regimes498.0ms

Accuracy

84.2% (1.3b remaining)

Error of 22.1b against oracle of 20.8b and baseline of 29.3b

bsearch3.0ms

simplify50.0ms

Iterations

Iter	Nodes
done	77
2	77
1	75
0	60

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.9s	3177×	body	1280	valid
1.3s	1190×	body	10240	exit
990.0ms	1663×	body	640	valid
640.0ms	698×	body	1280	nan
542.0ms	4583×	body	80	valid
482.0ms	5086×	body	80	nan
348.0ms	639×	body	640	nan
304.0ms	827×	body	320	valid
114.0ms	346×	body	320	nan
101.0ms	447×	body	160	valid
86.0ms	189×	body	160	nan