Details

sample297.0ms

Algorithm

intervals

Results

98.0ms	80×	body	1280	valid
94.0ms	31×	body	2560	valid
54.0ms	53×	body	640	valid
12.0ms	104×	body	80	valid
12.0ms	26×	body	320	valid
8.0ms	72×	body	80	nan
5.0ms	20×	body	160	valid

simplify651.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize22.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.1b	(pow (+ 1 (/ i n)) n)
0.7b	(- (pow (+ 1 (/ i n)) n) 1)
0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite483.0ms

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

203.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
178.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
72.0ms	(- (pow (+ 1 (/ i n)) n) 1)
13.0ms	(pow (+ 1 (/ i n)) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

425.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
397.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
262.0ms	(- (pow (+ 1 (/ i n)) n) 1)
227.0ms	(pow (+ 1 (/ i n)) n)

simplify990.0ms

Counts: 654 → 465

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize19.0ms

Local error

Found 4 expressions with local error:

11.7b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
6.1b	(pow (+ 1 (/ i n)) n)
0.4b	(/ 1 (/ i n))
0.4b	(/ (pow (+ 1 (/ i n)) n) (/ i n))

rewrite142.0ms

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

93.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
26.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)
6.0ms	(/ 1 (/ i n))

series989.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

365.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
343.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
267.0ms	(pow (+ 1 (/ i n)) n)
13.0ms	(/ 1 (/ i n))

simplify646.0ms

Counts: 511 → 324

prune3.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize30.0ms

Local error

Found 4 expressions with local error:

8.3b	(* n (* i i))
3.8b	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
0.4b	(* 1/6 (* n (* i i)))
0.1b	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))

rewrite785.0ms

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

509.0ms	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))
213.0ms	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
44.0ms	(* 1/6 (* n (* i i)))
18.0ms	(* n (* i i))

series197.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

73.0ms	(* 100 (+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2)))
57.0ms	(+ (+ (* 1/6 (* n (* i i))) n) (* (* n i) 1/2))
36.0ms	(* n (* i i))
30.0ms	(* 1/6 (* n (* i i)))

simplify454.0ms

Counts: 93 → 91

prune835.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize30.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* n (+ (* 50/3 (* i i)) 100)) (* 50 (* n i)))
3.3b	(* n (+ (* 50/3 (* i i)) 100))
0.3b	(* 50/3 (* i i))
0.2b	(* 50 (* n i))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

58.0ms	(* n (+ (* 50/3 (* i i)) 100))
37.0ms	(+ (* n (+ (* 50/3 (* i i)) 100)) (* 50 (* n i)))
20.0ms	(* 50/3 (* i i))
19.0ms	(* 50 (* n i))

series220.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(* n (+ (* 50/3 (* i i)) 100))
75.0ms	(+ (* n (+ (* 50/3 (* i i)) 100)) (* 50 (* n i)))
36.0ms	(* 50/3 (* i i))
26.0ms	(* 50 (* n i))

simplify488.0ms

Counts: 90 → 88

prune719.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.4b

regimes319.0ms

Accuracy

42.3% (15.8b remaining)

Error of 21.9b against oracle of 6.1b and baseline of 33.5b

bsearch482.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.4s	2450×	body	1280	valid
2.6s	964×	body	2560	valid
1.4s	1623×	body	640	valid
343.0ms	3139×	body	80	valid
340.0ms	869×	body	320	valid
280.0ms	2268×	body	80	nan
129.0ms	468×	body	160	valid
24.0ms	6×	body	5120	valid