Details

sample225.0ms

Algorithm

intervals

Results

92.0ms	83×	body	1280	valid
61.0ms	22×	body	2560	valid
28.0ms	51×	body	640	valid
11.0ms	35×	body	320	valid
10.0ms	110×	body	80	valid
7.0ms	76×	body	80	nan
2.0ms	8×	body	160	valid

simplify3.2s

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize16.0ms

Local error

Found 4 expressions with local error:

8.4b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
4.9b	(pow (+ 1 (/ i n)) n)
0.1b	(- (pow (+ 1 (/ i n)) n) 1)
0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite508.0ms

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:

Slowest

195.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
179.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
112.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

445.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
418.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
325.0ms	(- (pow (+ 1 (/ i n)) n) 1)
280.0ms	(pow (+ 1 (/ i n)) n)

simplify996.0ms

Counts: 465 → 465

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.0b

localize35.0ms

Local error

Found 4 expressions with local error:

9.5b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
4.9b	(pow (+ 1 (/ i n)) n)
0.2b	(/ 1 (/ i n))
0.2b	(/ (pow (+ 1 (/ i n)) n) (/ i n))

rewrite182.0ms

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:

Slowest

118.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
40.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)
8.0ms	(/ 1 (/ i n))

series829.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

343.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
263.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
213.0ms	(pow (+ 1 (/ i n)) n)
9.0ms	(/ 1 (/ i n))

simplify463.0ms

Counts: 324 → 324

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

6.6b	(* n (* i i))
4.5b	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
0.2b	(* 1/6 (* n (* i i)))
0.1b	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))

rewrite648.0ms

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×	`associate-l` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in`

Counts

4 → 79

Calls

4 calls:

Slowest

443.0ms	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))
152.0ms	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
32.0ms	(* 1/6 (* n (* i i)))
19.0ms	(* n (* i i))

series241.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))
78.0ms	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
39.0ms	(* 1/6 (* n (* i i)))
38.0ms	(* n (* i i))

simplify2.9s

Counts: 91 → 91

prune691.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* i 1/6)
0.1b	(* (* n i) (+ (* i 1/6) 1/2))
0.1b	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
0.0b	(+ n (* (* n i) (+ (* i 1/6) 1/2)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

Slowest

39.0ms	(* (* n i) (+ (* i 1/6) 1/2))
18.0ms	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
10.0ms	(+ n (* (* n i) (+ (* i 1/6) 1/2)))
7.0ms	(* i 1/6)

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
78.0ms	(* (* n i) (+ (* i 1/6) 1/2))
64.0ms	(+ n (* (* n i) (+ (* i 1/6) 1/2)))
20.0ms	(* i 1/6)

simplify3.7s

Counts: 91 → 91

prune659.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.5b

regimes531.0ms

Accuracy

52.9% (12.8b remaining)

Error of 18.8b against oracle of 6.0b and baseline of 33.2b

bsearch787.0ms

end0.0ms

sample9.5s

Algorithm

intervals

Results

3.4s	1011×	body	2560	valid
3.2s	2444×	body	1280	valid
1.1s	1612×	body	640	valid
689.0ms	3010×	body	80	valid
401.0ms	871×	body	320	valid
231.0ms	2279×	body	80	nan
119.0ms	460×	body	160	valid
37.0ms	8×	body	5120	valid