Details

sample235.0ms

Algorithm

intervals

Results

84.0ms	80×	body	1280	valid
71.0ms	29×	body	2560	valid
27.0ms	55×	body	640	valid
23.0ms	105×	body	80	valid
7.0ms	23×	body	320	valid
6.0ms	71×	body	80	nan
4.0ms	20×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	6722
5	1463
4	420
3	150
2	58
1	28
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize20.0ms

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)
7.5b	(pow (+ 1 (/ i n)) n)
9.7b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite451.0ms

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:

184.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
75.0ms	(- (pow (+ 1 (/ i n)) n) 1)
17.0ms	(pow (+ 1 (/ i n)) n)
164.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

334.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
267.0ms	(- (pow (+ 1 (/ i n)) n) 1)
261.0ms	(pow (+ 1 (/ i n)) n)
341.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.3s

Counts

465 → 465

Iterations

Iter	Nodes
2	5084
1	1658
0	542

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.4b	(/ 1 (/ i n))
7.5b	(pow (+ 1 (/ i n)) n)
11.9b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ 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:

27.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
6.0ms	(/ 1 (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)
94.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
10.0ms	(/ 1 (/ i n))
212.0ms	(pow (+ 1 (/ i n)) n)
292.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify835.0ms

Counts

324 → 324

Iterations

Iter	Nodes
2	3214
1	1200
0	487

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
0.2b	(* 1/6 (* n (* i i)))
3.0b	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
7.9b	(* n (* i i))

rewrite421.0ms

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:

44.0ms	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
324.0ms	(* 1/6 (* n (* i i)))
27.0ms	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
26.0ms	(* n (* i i))

series182.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
36.0ms	(* 1/6 (* n (* i i)))
56.0ms	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
29.0ms	(* n (* i i))

simplify3.5s

Counts

91 → 91

Iterations

Iter	Nodes
3	9098
2	1508
1	376
0	132

prune843.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ n (* (* n i) (+ (* i 1/6) 1/2)))
0.0b	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
0.1b	(* (* n i) (+ (* i 1/6) 1/2))
0.3b	(* i 1/6)

rewrite64.0ms

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:

10.0ms	(+ n (* (* n i) (+ (* i 1/6) 1/2)))
17.0ms	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
31.0ms	(* (* n i) (+ (* i 1/6) 1/2))
5.0ms	(* i 1/6)

series245.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ n (* (* n i) (+ (* i 1/6) 1/2)))
86.0ms	(* 100 (+ n (* (* n i) (+ (* i 1/6) 1/2))))
68.0ms	(* (* n i) (+ (* i 1/6) 1/2))
26.0ms	(* i 1/6)

simplify4.3s

Counts

91 → 91

Iterations

Iter	Nodes
3	9427
2	1531
1	414
0	144

prune569.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.4b

regimes339.0ms

Accuracy

56.6% (11.8b remaining)

Error of 17.9b against oracle of 6.1b and baseline of 33.4b

bsearch365.0ms

Steps

Iters	Range		Point
9	3.272698020116576	446233850.42817044	10.814933530045678
10	-141305917583818.8	-305.5104975057943	-310.361827324758

simplify6.0ms

Iterations

Iter	Nodes
2	44
1	44
0	32

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.5s	2525×	body	1280	valid
2.8s	945×	body	2560	valid
980.0ms	1614×	body	640	valid
363.0ms	3032×	body	80	valid
337.0ms	871×	body	320	valid
268.0ms	2195×	body	80	nan
128.0ms	447×	body	160	valid
51.0ms	11×	body	5120	valid