Details

sample294.0ms

Algorithm

intervals

Results

128.0ms	80×	body	1280	valid
82.0ms	28×	body	2560	valid
35.0ms	51×	body	640	valid
14.0ms	115×	body	80	valid
9.0ms	21×	body	320	valid
8.0ms	75×	body	80	nan
4.0ms	13×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	2696
4	553
3	154
2	58
1	28
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.3b	(- (pow (+ 1 (/ i n)) n) 1)
6.1b	(pow (+ 1 (/ i n)) n)
10.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `distribute-lft-out`

Counts

4 → 453

Calls

4 calls:

239.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
96.0ms	(- (pow (+ 1 (/ i n)) n) 1)
18.0ms	(pow (+ 1 (/ i n)) n)
219.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

334.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
273.0ms	(- (pow (+ 1 (/ i n)) n) 1)
322.0ms	(pow (+ 1 (/ i n)) n)
390.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.8s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	1702
0	542

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.3b	(/ 1 (/ i n))
6.1b	(pow (+ 1 (/ i n)) n)
12.4b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

395×	`times-frac`
286×	`add-sqr-sqrt`
233×	`*-un-lft-identity`
153×	`add-cube-cbrt`
70×	`unpow-prod-down`
35×	`difference-of-squares`
29×	`add-exp-log`
26×	`associate-/r*`
25×	`sqr-pow`
24×	`div-inv`
16×	`div-exp` `distribute-lft-out--`
15×	`distribute-lft-out`
14×	`add-cbrt-cube`
11×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `add-log-exp`
5×	`distribute-rgt-out--` `associate-/r/`
4×	`insert-posit16`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `pow-pow` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 312

Calls

4 calls:

41.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
10.0ms	(/ 1 (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)
118.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series942.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
10.0ms	(/ 1 (/ i n))
240.0ms	(pow (+ 1 (/ i n)) n)
399.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify2.0s

Counts

324 → 324

Iterations

Iter	Nodes
done	5014
2	3710
1	1236
0	487

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
0.2b	(* (* i i) 1/6)
3.5b	(+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n))
8.3b	(* n (* (* i i) 1/6))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in`

Counts

4 → 79

Calls

4 calls:

215.0ms	(* 100 (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
14.0ms	(* (* i i) 1/6)
57.0ms	(+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n))
37.0ms	(* n (* (* i i) 1/6))

series180.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 100 (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
28.0ms	(* (* i i) 1/6)
57.0ms	(+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n))
31.0ms	(* n (* (* i i) 1/6))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5007
2	1930
1	392
0	134

prune297.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.3b

localize38.0ms

Local error

Found 4 expressions with local error:

8.3b	(* n (* (* i i) 1/6))
12.6b	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
12.6b	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
12.6b	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+`
1×	`associate-r` `*-commutative`

Counts

4 → 64

Calls

4 calls:

36.0ms	(* n (* (* i i) 1/6))
53.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
54.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
56.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* n (* (* i i) 1/6))
118.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
121.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))
118.0ms	(cbrt (+ (* n (* (* i i) 1/6)) (+ (* (* n i) 1/2) n)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1235
1	310
0	120

prune352.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 5.3b

regimes378.0ms

Accuracy

56.6% (11.7b remaining)

Error of 17.8b against oracle of 6.1b and baseline of 33.1b

bsearch310.0ms

Steps

Iters	Range		Point
9	2.784564170770455e-12	0.0004981816479932727	0.0004866774544189746
8	-922.1020704437461	-0.5767180207385502	-1.8795028361709332

simplify10.0ms

Iterations

Iter	Nodes
done	47
1	47
0	34

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.4s	2514×	body	1280	valid
2.6s	1006×	body	2560	valid
1.1s	1632×	body	640	valid
578.0ms	3013×	body	80	valid
301.0ms	845×	body	320	valid
196.0ms	2294×	body	80	nan
98.0ms	440×	body	160	valid
31.0ms	8×	body	5120	valid