Details

sample322.0ms

Algorithm

intervals

Results

129.0ms	85×	body	1280	valid
100.0ms	28×	body	2560	valid
39.0ms	58×	body	640	valid
13.0ms	103×	body	80	valid
10.0ms	24×	body	320	valid
8.0ms	62×	body	80	nan
4.0ms	14×	body	160	valid

simplify3.4s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize30.0ms

Local error

Found 4 expressions with local error:

9.7b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
7.3b	(pow (+ 1 (/ i n)) n)
1.5b	(- (pow (+ 1 (/ i n)) n) 1)
0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite480.0ms

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

191.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
172.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
89.0ms	(- (pow (+ 1 (/ i n)) n) 1)
12.0ms	(pow (+ 1 (/ i n)) n)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

415.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
389.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
298.0ms	(pow (+ 1 (/ i n)) n)
262.0ms	(- (pow (+ 1 (/ i n)) n) 1)

simplify894.0ms

Counts: 465 → 465

prune5.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.1b

localize29.0ms

Local error

Found 4 expressions with local error:

18.1b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
7.3b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
0.1b	(* 1/6 (* i (* i i)))
0.1b	(* i (* i i))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
83×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
27×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
14×	`distribute-lft-out`
13×	`associate-/r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`flip3-+` `associate-r` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `cube-unmult` `associate-/r/` `pow-sqr` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

Slowest

183.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
63.0ms	(* 1/6 (* i (* i i)))
34.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
16.0ms	(* i (* i i))

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
97.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
57.0ms	(* 1/6 (* i (* i i)))
36.0ms	(* i (* i i))

simplify911.0ms

Counts: 158 → 158

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize23.0ms

Local error

Found 4 expressions with local error:

10.0b	(* (* i i) (* n 1/6))
5.0b	(+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))
0.4b	(* n 1/6)
0.1b	(* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6)))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`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:

Slowest

62.0ms	(* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6)))))
31.0ms	(+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))
27.0ms	(* (* i i) (* n 1/6))
9.0ms	(* n 1/6)

series200.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6)))))
67.0ms	(+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))
27.0ms	(* n 1/6)
24.0ms	(* (* i i) (* n 1/6))

simplify3.5s

Counts: 91 → 91

prune647.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.2b

localize36.0ms

Local error

Found 4 expressions with local error:

11.1b	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
11.1b	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
11.1b	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
10.0b	(* (* i i) (* n 1/6))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

24.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
22.0ms	(* (* i i) (* n 1/6))
19.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
19.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
156.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
152.0ms	(cbrt (* 100 (+ (* 1/2 (* n i)) (+ n (* (* i i) (* n 1/6))))))
23.0ms	(* (* i i) (* n 1/6))

simplify1.9s

Counts: 71 → 71

prune776.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.2b

regimes359.0ms

Accuracy

49.6% (11.4b remaining)

Error of 22.3b against oracle of 10.9b and baseline of 33.5b

bsearch821.0ms

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.8s	2511×	body	1280	valid
2.5s	987×	body	2560	valid
1.4s	1624×	body	640	valid
417.0ms	3058×	body	80	valid
317.0ms	846×	body	320	valid
198.0ms	2211×	body	80	nan
114.0ms	420×	body	160	valid
23.0ms	5×	body	5120	valid