Details

sample362.0ms

Algorithm

intervals

Results

146.0ms	37×	body	2560	valid
110.0ms	70×	body	1280	valid
47.0ms	57×	body	640	valid
19.0ms	35×	body	320	valid
12.0ms	83×	body	80	valid
8.0ms	62×	body	80	nan
4.0ms	12×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2473
4	512
3	150
2	58
1	28
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
2.4b	(- (pow (+ 1 (/ i n)) n) 1)
4.6b	(pow (+ 1 (/ i n)) n)
11.4b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite490.0ms

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:

202.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
73.0ms	(- (pow (+ 1 (/ i n)) n) 1)
17.0ms	(pow (+ 1 (/ i n)) n)
188.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

415.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
312.0ms	(- (pow (+ 1 (/ i n)) n) 1)
297.0ms	(pow (+ 1 (/ i n)) n)
412.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.8s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	1702
0	542

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.3b	(* 1/6 (* i (* i i)))
4.8b	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
16.5b	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

14.0ms	(* i (* i i))
32.0ms	(* 1/6 (* i (* i i)))
85.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
292.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

series218.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* i (* i i))
52.0ms	(* 1/6 (* i (* i i)))
36.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
76.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

simplify1.8s

Counts

146 → 146

Iterations

Iter	Nodes
done	5005
2	2329
1	627
0	238

prune738.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 12.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* i 1/6)
2.7b	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
4.5b	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
4.8b	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
8×	`pow1`
6×	`associate-r`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `associate-*l/`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* i 1/6)
430.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
70.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
23.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* i 1/6)
84.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
68.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
42.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1497
1	409
0	156

prune513.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 i) (* 1/6 (* i i)))
0.1b	(* 100 (+ n (* n (+ (* 1/2 i) (* 1/6 (* i i))))))
0.3b	(* 1/6 (* i i))
2.7b	(* n (+ (* 1/2 i) (* 1/6 (* i i))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

8.0ms	(+ (* 1/2 i) (* 1/6 (* i i)))
14.0ms	(* 100 (+ n (* n (+ (* 1/2 i) (* 1/6 (* i i))))))
13.0ms	(* 1/6 (* i i))
23.0ms	(* n (+ (* 1/2 i) (* 1/6 (* i i))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (* 1/2 i) (* 1/6 (* i i)))
88.0ms	(* 100 (+ n (* n (+ (* 1/2 i) (* 1/6 (* i i))))))
37.0ms	(* 1/6 (* i i))
117.0ms	(* n (+ (* 1/2 i) (* 1/6 (* i i))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5006
2	1868
1	456
0	140

prune258.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.2b

regimes482.0ms

Accuracy

55.3% (10.2b remaining)

Error of 21.0b against oracle of 10.8b and baseline of 33.7b

bsearch411.0ms

Steps

Iters	Range		Point
10	6.842741084471096e-144	2.1628673624658724e-133	1.2083195710773826e-138
10	-3168283.462966651	-7.008719073765952e-13	-0.574841385015252
5	-1.879209070390038e+69	-4.998514185092426e+68	-6.429664273656172e+68
6	-3.42871200991951e+95	-4.7552491283276806e+94	-6.470021336482934e+94

simplify7.0ms

Iterations

Iter	Nodes
done	46
1	46
0	33

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.9s	2449×	body	1280	valid
2.5s	969×	body	2560	valid
955.0ms	1660×	body	640	valid
721.0ms	3052×	body	80	valid
316.0ms	850×	body	320	valid
264.0ms	2271×	body	80	nan
97.0ms	432×	body	160	valid
37.0ms	10×	body	5120	valid