Details

sample352.0ms

Algorithm

intervals

Results

105.0ms	106×	body	1280	valid
38.0ms	36×	body	10240	exit
37.0ms	43×	body	640	valid
23.0ms	18×	body	1280	nan
21.0ms	159×	body	80	valid
21.0ms	196×	body	80	nan
13.0ms	21×	body	640	nan
9.0ms	18×	body	320	valid
7.0ms	20×	body	160	valid
5.0ms	9×	body	320	nan
3.0ms	9×	body	160	nan

simplify7.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3086
5	673
4	238
3	86
2	35
1	17
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize74.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
3.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite341.0ms

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:

9.0ms	(pow x (/ 1.0 n))
47.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series883.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(pow x (/ 1.0 n))
252.0ms	(pow (+ x 1.0) (/ 1.0 n))
516.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify4.4s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	1891
1	714
0	273

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize407.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt x) (/ 1.0 n))
1.2b	(pow (+ 1.0 x) (/ 1.0 n))
2.7b	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`pow-unpow`
25×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down` `times-frac`
8×	`fma-neg` `prod-diff`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-prod` `pow-pow` `distribute-lft-out`
2×	`pow-to-exp` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `fma-udef` `flip--`

Counts

4 → 107

Calls

4 calls:

21.0ms	(pow (cbrt x) (/ 1.0 n))
42.0ms	(pow (+ 1.0 x) (/ 1.0 n))
2.0ms	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
228.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series3.4s

Counts

4 → 12

Calls

4 calls:

207.0ms	(pow (cbrt x) (/ 1.0 n))
270.0ms	(pow (+ 1.0 x) (/ 1.0 n))
1.8s	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.1s	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

simplify6.1s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2414
1	770
0	269

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.4b

localize637.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite768.0ms

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:

3.0ms	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
258.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
258.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
237.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series4.8s

Counts

4 → 12

Calls

4 calls:

1.8s	(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.1s	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.0s	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
920.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

simplify4.6s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
2	1572
1	482
0	182

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.4b

localize454.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ 1.0 x) (/ 1.0 n))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
3.5b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite770.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
28×	`unpow-prod-down`
24×	`add-sqr-sqrt` `fma-neg` `prod-diff` `add-cube-cbrt`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out` `sqr-pow`
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 → 124

Calls

4 calls:

19.0ms	(pow (+ 1.0 x) (/ 1.0 n))
247.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
257.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
232.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series3.3s

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow (+ 1.0 x) (/ 1.0 n))
1.0s	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
995.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
985.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

simplify4.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5016
2	2029
1	620
0	211

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.4b

regimes1.1s

Accuracy

75.3% (2.1b remaining)

Error of 23.2b against oracle of 21.1b and baseline of 29.4b

bsearch7.0ms

simplify32.0ms

Iterations

Iter	Nodes
done	53
1	53
0	43

end0.0ms

sample9.5s

Algorithm

intervals

Results

2.9s	3157×	body	1280	valid
1.5s	1604×	body	640	valid
1.5s	1103×	body	10240	exit
706.0ms	4596×	body	80	valid
539.0ms	604×	body	1280	nan
479.0ms	5081×	body	80	nan
442.0ms	838×	body	320	valid
429.0ms	634×	body	640	nan
201.0ms	349×	body	320	nan
126.0ms	459×	body	160	valid
41.0ms	178×	body	160	nan