Details

sample240.0ms

Algorithm

intervals

Results

93.0ms	98×	body	1280	valid
28.0ms	38×	body	10240	exit
23.0ms	41×	body	640	valid
19.0ms	166×	body	80	valid
15.0ms	21×	body	1280	nan
15.0ms	175×	body	80	nan
12.0ms	16×	body	640	nan
9.0ms	25×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	10×	body	160	nan
1.0ms	4×	body	320	nan

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2099
6	2099
5	1210
4	275
3	89
2	37
1	19
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite132.0ms

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))
10.0ms	(pow (+ x 1) (/ 1 n))
116.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series389.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(pow x (/ 1 n))
87.0ms	(pow (+ x 1) (/ 1 n))
220.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.2s

Counts

161 → 161

Iterations

Iter	Nodes
done	2000
3	2000
2	1649
1	651
0	257

prune648.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.3b

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite324.0ms

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:

12.0ms	(pow (+ x 1) (/ 1 n))
81.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
117.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
106.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow (+ x 1) (/ 1 n))
216.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
250.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
259.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.6s

Counts

316 → 316

Iterations

Iter	Nodes
done	2001
3	2001
2	1287
1	543
0	221

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.2b

localize86.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
3.9b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
114×	`*-un-lft-identity`
112×	`prod-diff`
92×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
44×	`sqr-pow`
18×	`distribute-lft-out` `difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--`

Counts

4 → 204

Calls

4 calls:

77.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
66.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
1.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

series1.3s

Counts

4 → 12

Calls

4 calls:

234.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
269.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
455.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
365.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

simplify1.7s

Counts

216 → 216

Iterations

Iter	Nodes
done	2004
3	2004
2	1810
1	642
0	277

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.2b

localize191.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.0b	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.0b	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
3.9b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`unpow-prod-down` `fma-neg` `prod-diff`
16×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-log-exp`
6×	`distribute-lft-out` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`fma-udef`

Counts

4 → 104

Calls

4 calls:

53.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
75.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
83.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
0.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

series1.7s

Counts

4 → 12

Calls

4 calls:

509.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
458.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
427.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
349.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	2008
3	2008
2	1299
1	406
0	162

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.2b

regimes399.0ms

Accuracy

90% (1.1b remaining)

Error of 19.1b against oracle of 18.0b and baseline of 29.2b

bsearch2.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	73
2	73
1	69
0	53

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.2s	3100×	body	1280	valid
1.3s	1174×	body	10240	exit
1.2s	1632×	body	640	valid
1.1s	4700×	body	80	valid
931.0ms	690×	body	640	nan
700.0ms	649×	body	1280	nan
563.0ms	5090×	body	80	nan
501.0ms	873×	body	320	valid
194.0ms	362×	body	320	nan
133.0ms	443×	body	160	valid
56.0ms	210×	body	160	nan