Details

sample308.0ms

Algorithm

intervals

Results

119.0ms	109×	body	1280	valid
37.0ms	47×	body	640	valid
32.0ms	28×	body	10240	exit
22.0ms	154×	body	80	valid
19.0ms	176×	body	80	nan
16.0ms	22×	body	640	nan
15.0ms	31×	body	320	valid
13.0ms	16×	body	1280	nan
5.0ms	15×	body	160	valid
4.0ms	9×	body	320	nan
2.0ms	5×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1377
4	296
3	89
2	37
1	19
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite109.0ms

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))
96.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series532.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(pow x (/ 1 n))
126.0ms	(pow (+ x 1) (/ 1 n))
298.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.5s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	1805
1	651
0	257

prune719.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.3b

localize100.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ (/ 1 n) 2))
1.0b	(pow (+ x 1) (/ (/ 1 n) 2))
2.2b	(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))))
3.8b	(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)))))

rewrite39.0ms

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:

16.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
16.0ms	(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))))
1.0ms	(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)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
95.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
335.0ms	(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))))
952.0ms	(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)))))

simplify1.9s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
2	2452
1	732
0	257

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize133.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.1b	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.1b	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.2b	(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))))

rewrite235.0ms

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:

87.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
77.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
68.0ms	(- (pow (+ 1 x) (/ 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:

468.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
467.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
410.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
391.0ms	(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))))

simplify2.6s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1335
1	406
0	162

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize125.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
2.1b	(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
2.2b	(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))))
2.2b	(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))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

77.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
0.0ms	(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (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))))
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:

484.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
471.0ms	(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
375.0ms	(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))))
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))))

simplify2.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
2	1414
1	427
0	173

prune806.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.2b

regimes452.0ms

Accuracy

87.1% (1.6b remaining)

Error of 19.2b against oracle of 17.6b and baseline of 29.9b

bsearch1.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	59
2	59
1	57
0	44

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.2s	3267×	body	1280	valid
1.3s	1141×	body	10240	exit
1.2s	1580×	body	640	valid
736.0ms	631×	body	1280	nan
716.0ms	4594×	body	80	valid
630.0ms	4931×	body	80	nan
604.0ms	686×	body	640	nan
445.0ms	838×	body	320	valid
166.0ms	353×	body	320	nan
141.0ms	444×	body	160	valid
84.0ms	182×	body	160	nan