Details

sample264.0ms

Algorithm

intervals

Results

83.0ms	97×	body	1280	valid
37.0ms	52×	body	640	valid
27.0ms	146×	body	80	valid
23.0ms	30×	body	10240	exit
19.0ms	21×	body	1280	nan
15.0ms	134×	body	80	nan
14.0ms	20×	body	640	nan
14.0ms	27×	body	320	valid
4.0ms	17×	body	160	valid
4.0ms	7×	body	320	nan
1.0ms	5×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2068
6	2068
5	1169
4	263
3	84
2	36
1	19
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize24.0ms

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

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 82

Calls

3 calls:

5.0ms	(pow x (/ 1 n))
12.0ms	(pow (+ x 1) (/ 1 n))
65.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series453.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(pow x (/ 1 n))
88.0ms	(pow (+ x 1) (/ 1 n))
274.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
3	2003
2	1224
1	473
0	176

prune449.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1 n) 2))
0.7b	(pow x (/ (/ 1 n) 2))
1.2b	(pow (+ x 1) (/ 1 n))
3.8b	(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
99×	`pow-unpow`
86×	`add-sqr-sqrt` `*-un-lft-identity`
84×	`add-cube-cbrt`
11×	`unpow-prod-down`
9×	`div-inv`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 161

Calls

4 calls:

4.0ms	(pow x (/ (/ 1 n) 2))
3.0ms	(pow x (/ (/ 1 n) 2))
7.0ms	(pow (+ x 1) (/ 1 n))
91.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

93.0ms	(pow x (/ (/ 1 n) 2))
548.0ms	(pow x (/ (/ 1 n) 2))
109.0ms	(pow (+ x 1) (/ 1 n))
362.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))

simplify1.6s

Counts

173 → 173

Iterations

Iter	Nodes
done	2000
3	2000
2	1903
1	736
0	246

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* n x))
0.5b	(/ 1 (* n x))
3.3b	(+ (/ 1 (* n x)) (* (/ (log x) n) (/ 1 (* n x))))
7.6b	(* (* x x) n)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
19×	`add-cbrt-cube`
15×	`pow1`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-exp` `add-cube-cbrt`
8×	`div-exp`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`pow-prod-down` `cbrt-unprod`
4×	`cbrt-undiv` `rec-exp` `1-exp` `frac-add` `insert-posit16` `pow-flip`
3×	`associate-r` `div-inv`
2×	`clear-num` `associate-/r*` `frac-2neg` `distribute-rgt-out` `inv-pow`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `associate-l` `associate-l/` `distribute-rgt1-in` `associate-r/` `un-div-inv` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

16.0ms	(/ 1 (* n x))
17.0ms	(/ 1 (* n x))
34.0ms	(+ (/ 1 (* n x)) (* (/ (log x) n) (/ 1 (* n x))))
40.0ms	(* (* x x) n)

series168.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (* n x))
20.0ms	(/ 1 (* n x))
97.0ms	(+ (/ 1 (* n x)) (* (/ (log x) n) (/ 1 (* n x))))
33.0ms	(* (* x x) n)

simplify1.3s

Counts

109 → 109

Iterations

Iter	Nodes
done	2008
3	2008
2	1683
1	401
0	137

prune464.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 n) (/ 1 x))
0.5b	(/ 1 (* n x))
3.3b	(+ (* (/ 1 n) (/ 1 x)) (* (/ (log x) n) (/ 1 (* n x))))
7.6b	(* (* x x) n)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
46×	`add-sqr-sqrt`
33×	`times-frac`
27×	`*-un-lft-identity`
26×	`add-cbrt-cube`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`div-exp`
16×	`pow1` `associate-r` `frac-add`
14×	`associate-l`
10×	`rec-exp` `1-exp` `unswap-sqr`
9×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
8×	`cbrt-unprod`
7×	`pow-prod-down`
6×	`cbrt-undiv` `add-log-exp`
4×	`insert-posit16` `pow-flip`
3×	`div-inv` `associate-/l*` `inv-pow`
2×	`*-commutative`
1×	`+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip-+`

Counts

4 → 148

Calls

4 calls:

14.0ms	(* (/ 1 n) (/ 1 x))
11.0ms	(/ 1 (* n x))
30.0ms	(+ (* (/ 1 n) (/ 1 x)) (* (/ (log x) n) (/ 1 (* n x))))
27.0ms	(* (* x x) n)

series121.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ 1 n) (/ 1 x))
11.0ms	(/ 1 (* n x))
64.0ms	(+ (* (/ 1 n) (/ 1 x)) (* (/ (log x) n) (/ 1 (* n x))))
29.0ms	(* (* x x) n)

simplify1.2s

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
2	2000
1	799
0	265

prune684.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.2b

regimes379.0ms

Accuracy

82.6% (1.5b remaining)

Error of 22.1b against oracle of 20.6b and baseline of 29.4b

bsearch286.0ms

Steps

Iters	Range		Point
6	1666127661722.954	10191059846820.299	1688833050023.4038
10	-190824653340.76273	-0.004172822113657255	-9979728547.756907

simplify20.0ms

Iterations

Iter	Nodes
done	48
1	48
0	38

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.9s	3136×	body	1280	valid
1.2s	1607×	body	640	valid
1.2s	1150×	body	10240	exit
763.0ms	4762×	body	80	valid
650.0ms	4935×	body	80	nan
649.0ms	595×	body	1280	nan
578.0ms	632×	body	640	nan
462.0ms	839×	body	320	valid
200.0ms	459×	body	160	valid
179.0ms	322×	body	320	nan
103.0ms	177×	body	160	nan