Details

sample306.0ms

Algorithm

intervals

Results

123.0ms	120×	body	1280	valid
32.0ms	49×	body	640	valid
30.0ms	36×	body	10240	exit
21.0ms	20×	body	1280	nan
17.0ms	145×	body	80	valid
16.0ms	162×	body	80	nan
15.0ms	23×	body	640	nan
14.0ms	29×	body	320	valid
9.0ms	19×	body	320	nan
6.0ms	20×	body	160	valid
3.0ms	10×	body	160	nan

simplify722.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2013
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: 27.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow x (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite106.0ms

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:

3.0ms	(pow x (/ 1 n))
8.0ms	(pow (+ x 1) (/ 1 n))
93.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series417.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(pow x (/ 1 n))
97.0ms	(pow (+ x 1) (/ 1 n))
244.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.0s

Counts

161 → 161

Iterations

Iter	Nodes
done	2000
2	1649
1	651
0	257

prune801.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1) (/ 1 n))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite252.0ms

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:

7.0ms	(pow (+ x 1) (/ 1 n))
73.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
104.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
63.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series893.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(pow (+ x 1) (/ 1 n))
304.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
255.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
212.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify886.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	2001
2	1287
1	543
0	221

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.9b

localize76.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite327.0ms

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:

97.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
68.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
88.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
63.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

283.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
272.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
230.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
262.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify785.0ms

Counts

376 → 376

Iterations

Iter	Nodes
done	2002
2	854
1	385
0	176

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.9b

localize53.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.2b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 362

Calls

4 calls:

70.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
63.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
73.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
149.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

283.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
266.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
260.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
224.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

simplify1.0s

Counts

374 → 374

Iterations

Iter	Nodes
done	2000
2	1142
1	571
0	336

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.9b

regimes518.0ms

Accuracy

89.2% (1.3b remaining)

Error of 19.2b against oracle of 17.9b and baseline of 29.5b

bsearch1.1s

Steps

Iters	Range		Point
9	251738.59665303899	941504501108.8118	792592107.1486229
11	-1.0180184649015773e-306	2.8429787932639455e-282	-4.76046101311837e-310
5	-3667221935386926.0	-1629780213615114.5	-1982989920422248.0

simplify61.0ms

Iterations

Iter	Nodes
done	71
2	71
1	65
0	50

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.4s	3224×	body	1280	valid
1.7s	1175×	body	10240	exit
1.3s	1598×	body	640	valid
770.0ms	666×	body	1280	nan
734.0ms	4703×	body	80	valid
693.0ms	5182×	body	80	nan
534.0ms	651×	body	640	nan
449.0ms	186×	body	160	nan
426.0ms	849×	body	320	valid
182.0ms	396×	body	320	nan
137.0ms	448×	body	160	valid