Details

sample215.0ms

Algorithm

intervals

Results

91.0ms	109×	body	1280	valid
23.0ms	47×	body	640	valid
23.0ms	28×	body	10240	exit
13.0ms	154×	body	80	valid
10.0ms	31×	body	320	valid
10.0ms	22×	body	640	nan
10.0ms	176×	body	80	nan
8.0ms	16×	body	1280	nan
3.0ms	15×	body	160	valid
3.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1210
4	275
3	89
2	37
1	19
0	8

prune5.0ms

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)))

rewrite114.0ms

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:

4.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
101.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series436.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(pow x (/ 1 n))
109.0ms	(pow (+ x 1) (/ 1 n))
249.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.1s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	1649
1	651
0	257

prune597.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize62.0ms

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)))))

rewrite25.0ms

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:

14.0ms	(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)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

101.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
120.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
367.0ms	(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))))
538.0ms	(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)))))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5003
2	2237
1	732
0	257

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.7b

localize129.0ms

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))))

rewrite233.0ms

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:

94.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
74.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
63.0ms	(- (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))))

series1.8s

Counts

4 → 12

Calls

4 calls:

505.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
394.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
513.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
393.0ms	(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))))

simplify2.9s

Counts

116 → 116

Iterations

Iter	Nodes
done	5003
2	1299
1	406
0	162

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.7b

localize146.0ms

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))))

rewrite59.0ms

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:

58.0ms	(- (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:

453.0ms	(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
505.0ms	(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
364.0ms	(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))))
380.0ms	(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

76 → 76

Iterations

Iter	Nodes
done	5000
2	1384
1	427
0	173

prune786.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.7b

regimes440.0ms

Accuracy

86.7% (1.6b remaining)

Error of 19.6b against oracle of 18.0b and baseline of 29.9b

bsearch2.0ms

simplify24.0ms

Iterations

Iter	Nodes
done	59
2	59
1	57
0	45

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	3267×	body	1280	valid
1.4s	1141×	body	10240	exit
997.0ms	1580×	body	640	valid
892.0ms	4594×	body	80	valid
631.0ms	631×	body	1280	nan
474.0ms	686×	body	640	nan
408.0ms	4931×	body	80	nan
327.0ms	838×	body	320	valid
144.0ms	444×	body	160	valid
116.0ms	353×	body	320	nan
34.0ms	182×	body	160	nan