Details

sample242.0ms

Algorithm

intervals

Results

75.0ms	102×	body	1280	valid
35.0ms	45×	body	10240	exit
32.0ms	55×	body	640	valid
20.0ms	19×	body	1280	nan
13.0ms	144×	body	80	valid
12.0ms	24×	body	640	nan
12.0ms	183×	body	80	nan
11.0ms	29×	body	320	valid
4.0ms	11×	body	320	nan
4.0ms	13×	body	160	valid
1.0ms	4×	body	160	nan

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1210
4	275
3	89
2	37
1	19
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite143.0ms

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` `insert-posit16` `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 → 152

Calls

3 calls:

5.0ms	(pow x (/ 1 n))
12.0ms	(pow (+ x 1) (/ 1 n))
120.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series517.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(pow x (/ 1 n))
139.0ms	(pow (+ x 1) (/ 1 n))
301.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	1649
1	651
0	257

prune797.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite360.0ms

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` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 304

Calls

4 calls:

20.0ms	(pow (+ x 1) (/ 1 n))
106.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
104.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
110.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series889.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (+ x 1) (/ 1 n))
259.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
273.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
245.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.7s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
3	4376
2	1287
1	543
0	221

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize76.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.5b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

136×	`unpow-prod-down`
124×	`*-un-lft-identity`
112×	`prod-diff`
100×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv`

Counts

4 → 224

Calls

4 calls:

14.0ms	(pow (+ x 1) (/ 1 n))
175.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
103.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow (+ x 1) (/ 1 n))
234.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
209.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
393.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

simplify3.1s

Counts

236 → 236

Iterations

Iter	Nodes
done	5000
3	4305
2	1434
1	579
0	236

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize84.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

264×	`unpow-prod-down`
224×	`*-un-lft-identity` `prod-diff`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
88×	`sqr-pow`
36×	`distribute-lft-out` `difference-of-squares`
32×	`fma-neg`
12×	`distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

4 → 364

Calls

4 calls:

128.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
145.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
145.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
137.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

262.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
263.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
243.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
274.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.1s

Counts

376 → 376

Iterations

Iter	Nodes
done	5002
3	2756
2	854
1	385
0	176

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

regimes485.0ms

Accuracy

87.4% (1.5b remaining)

Error of 19.5b against oracle of 18.1b and baseline of 29.6b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	47
1	47
0	38

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	3060×	body	1280	valid
1.3s	1584×	body	640	valid
1.1s	1135×	body	10240	exit
1.0s	685×	body	1280	nan
543.0ms	4768×	body	80	valid
389.0ms	5008×	body	80	nan
355.0ms	640×	body	640	nan
341.0ms	920×	body	320	valid
170.0ms	376×	body	320	nan
103.0ms	452×	body	160	valid
38.0ms	187×	body	160	nan