Details

sample271.0ms

Algorithm

intervals

Results

84.0ms	97×	body	1280	valid
37.0ms	52×	body	640	valid
34.0ms	27×	body	320	valid
21.0ms	30×	body	10240	exit
20.0ms	21×	body	1280	nan
20.0ms	146×	body	80	valid
13.0ms	134×	body	80	nan
13.0ms	20×	body	640	nan
5.0ms	17×	body	160	valid
3.0ms	7×	body	320	nan
1.0ms	5×	body	160	nan

simplify1.2s

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: 27.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1 n))
1.2b	(pow (+ x 1) (/ 1 n))
2.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite85.0ms

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:

6.0ms	(pow x (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
61.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series437.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1 n))
98.0ms	(pow (+ x 1) (/ 1 n))
276.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.3s

Counts

161 → 161

Iterations

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

prune747.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize64.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1) (/ (/ 1 n) 2))
1.2b	(pow (+ x 1) (/ (/ 1 n) 2))
1.5b	(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))))
3.5b	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
86×	`pow-unpow`
80×	`*-un-lft-identity`
76×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`unpow-prod-down` `div-inv`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

10.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
8.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
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))))
0.0ms	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

112.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
127.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
418.0ms	(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))))
526.0ms	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify1.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	2003
2	2003
1	732
0	257

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.2b

localize93.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1) (/ (/ 1 n) 2))
1.2b	(pow (+ x 1) (/ (/ 1 n) 2))
1.5b	(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))))
3.5b	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
86×	`pow-unpow`
80×	`*-un-lft-identity`
76×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`unpow-prod-down` `div-inv`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

13.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
23.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
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))))
0.0ms	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
116.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
361.0ms	(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))))
551.0ms	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify1.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	2003
2	2003
1	732
0	257

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 n) (log1p x))
0.7b	(pow x (/ 1 n))
2.3b	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
33×	`add-cube-cbrt`
21×	`prod-diff`
20×	`times-frac`
13×	`pow-unpow` `unpow-prod-down` `associate-l` `add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp` `sqr-pow`
4×	`prod-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `insert-posit16` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
2×	`div-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `rec-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `flip--` `distribute-lft-out--`

Counts

3 → 111

Calls

3 calls:

18.0ms	(* (/ 1 n) (log1p x))
5.0ms	(pow x (/ 1 n))
36.0ms	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ 1 n) (log1p x))
67.0ms	(pow x (/ 1 n))
201.0ms	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))

simplify1.3s

Counts

120 → 120

Iterations

Iter	Nodes
done	2001
3	2001
2	1725
1	679
0	265

prune611.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.1b

regimes497.0ms

Accuracy

75.3% (3.0b remaining)

Error of 20.7b against oracle of 17.8b and baseline of 29.8b

bsearch3.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	66
2	66
1	62
0	49

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.6s	3136×	body	1280	valid
1.3s	1150×	body	10240	exit
1.2s	1607×	body	640	valid
1.2s	4762×	body	80	valid
877.0ms	839×	body	320	valid
709.0ms	595×	body	1280	nan
616.0ms	632×	body	640	nan
539.0ms	4935×	body	80	nan
171.0ms	322×	body	320	nan
152.0ms	459×	body	160	valid
54.0ms	177×	body	160	nan