Details

sample282.0ms

Algorithm

intervals

Results

79.0ms	100×	body	1280	valid
36.0ms	43×	body	10240	exit
34.0ms	12×	body	320	nan
31.0ms	51×	body	640	valid
17.0ms	170×	body	80	valid
11.0ms	171×	body	80	nan
11.0ms	29×	body	320	valid
10.0ms	14×	body	1280	nan
9.0ms	15×	body	640	nan
3.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify6.9s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize40.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `div-inv` `flip--`

Counts

2 → 122

Calls

2 calls:

15.0ms	(pow (+ x 1.0) (/ 1.0 n))
155.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series812.0ms

Counts

2 → 6

Calls

2 calls:

275.0ms	(pow (+ x 1.0) (/ 1.0 n))
537.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify7.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
3	4901
2	1526
1	595
0	235

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2)))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.0b	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
104×	`*-un-lft-identity`
100×	`add-sqr-sqrt`
86×	`pow-unpow` `add-cube-cbrt`
38×	`unpow-prod-down`
18×	`add-exp-log`
14×	`sqr-pow`
10×	`swap-sqr`
9×	`prod-exp` `unswap-sqr`
8×	`pow-to-exp` `associate-r` `associate-l` `pow-exp` `div-inv` `distribute-lft-out`
7×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow-pow`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--`

Counts

4 → 208

Calls

4 calls:

129.0ms	(* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2)))
36.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
20.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
80.0ms	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

series1.9s

Counts

4 → 12

Calls

4 calls:

471.0ms	(* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2)))
296.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
294.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
817.0ms	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

simplify4.8s

Counts

220 → 220

Iterations

Iter	Nodes
done	5001
2	2584
1	893
0	310

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.6b

localize222.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.7b	(pow (+ 1.0 x) (/ 1.0 n))
1.7b	(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))))
2.0b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

3.0ms	(cbrt x)
29.0ms	(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))))
168.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series3.5s

Counts

4 → 12

Calls

4 calls:

333.0ms	(cbrt x)
277.0ms	(pow (+ 1.0 x) (/ 1.0 n))
1.9s	(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))))

simplify4.8s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
2	2067
1	648
0	238

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (+ 1.0 x) (/ 1.0 n))
2.0b	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
28.0ms	(pow (+ 1.0 x) (/ 1.0 n))
188.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series1.9s

Counts

4 → 12

Calls

4 calls:

346.0ms	(cbrt x)
310.0ms	(cbrt x)
288.0ms	(pow (+ 1.0 x) (/ 1.0 n))
979.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

simplify4.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2058
1	636
0	224

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

regimes930.0ms

Accuracy

90.6% (1.8b remaining)

Error of 22.4b against oracle of 20.6b and baseline of 39.9b

bsearch325.0ms

Steps

Iters	Range		Point
10	0.00018705152818348546	24130438545.104744	353.8529854336742
8	-351300497490.8783	-26711381.42537418	-27159841.04125247

simplify14.0ms

Iterations

Iter	Nodes
done	46
1	46
0	35

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.3s	3175×	body	1280	valid
1.0s	4651×	body	80	valid
900.0ms	1569×	body	640	valid
817.0ms	1179×	body	10240	exit
805.0ms	626×	body	1280	nan
412.0ms	846×	body	320	valid
405.0ms	631×	body	640	nan
303.0ms	5178×	body	80	nan
154.0ms	443×	body	160	valid
105.0ms	354×	body	320	nan
29.0ms	166×	body	160	nan