Details

sample215.0ms

Algorithm

intervals

Results

80.0ms	33×	body	2560	valid
78.0ms	72×	body	1280	valid
23.0ms	54×	body	640	valid
9.0ms	34×	body	320	valid
6.0ms	90×	body	80	valid
3.0ms	54×	body	80	nan
2.0ms	14×	body	160	valid

simplify1.7s

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: 44.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
0.7b	(- (pow (+ 1 (/ i n)) n) 1)
5.3b	(pow (+ 1 (/ i n)) n)
10.7b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite1.1s

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:

475.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
200.0ms	(- (pow (+ 1 (/ i n)) n) 1)
34.0ms	(pow (+ 1 (/ i n)) n)
339.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

439.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
280.0ms	(- (pow (+ 1 (/ i n)) n) 1)
302.0ms	(pow (+ 1 (/ i n)) n)
382.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.6s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	1702
0	542

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.1b	(* 1/6 (* i (* i i)))
6.0b	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
17.2b	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

rewrite614.0ms

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:

24.0ms	(* i (* i i))
44.0ms	(* 1/6 (* i (* i i)))
119.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
420.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

series244.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* i (* i i))
47.0ms	(* 1/6 (* i (* i i)))
39.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
104.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

simplify1.9s

Counts

146 → 146

Iterations

Iter	Nodes
done	5005
2	2329
1	627
0	238

prune598.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
0.1b	(* (* i i) 1/6)
2.5b	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
9.4b	(* (* (* i i) 1/6) n)

rewrite409.0ms

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-r` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`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:

262.0ms	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
17.0ms	(* (* i i) 1/6)
60.0ms	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
69.0ms	(* (* (* i i) 1/6) n)

series143.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
36.0ms	(* (* i i) 1/6)
40.0ms	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
31.0ms	(* (* (* i i) 1/6) n)

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	5005
2	1805
1	398
0	136

prune489.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
0.1b	(* i (* i 1/6))
0.4b	(* i 1/6)
3.5b	(* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i)))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

247.0ms	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
17.0ms	(* i (* i 1/6))
10.0ms	(* i 1/6)
257.0ms	(* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
35.0ms	(* i (* i 1/6))
27.0ms	(* i 1/6)
87.0ms	(* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i)))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5014
2	1899
1	412
0	140

prune310.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.9b

regimes411.0ms

Accuracy

54.5% (10.3b remaining)

Error of 21.3b against oracle of 11.1b and baseline of 33.6b

bsearch360.0ms

Steps

Iters	Range	Point
8	5.088358115576262e-115	1.391186477839907e-110	6.743108364226336e-114
10	-1.4244285555183042e-05	-9.550132857780223e-23	-1.1163211071803005e-19
8	-1.8459945982333864e+87	-1.5672427741481648e+83	-4.919477946002002e+83

Iters

Range

Point

5.088358115576262e-115

1.391186477839907e-110

6.743108364226336e-114

-1.4244285555183042e-05

-9.550132857780223e-23

-1.1163211071803005e-19

-1.8459945982333864e+87

-1.5672427741481648e+83

-4.919477946002002e+83

simplify6.0ms

Iterations

Iter	Nodes
done	42
1	42
0	31

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.3s	2503×	body	1280	valid
2.1s	941×	body	2560	valid
860.0ms	1621×	body	640	valid
477.0ms	3022×	body	80	valid
189.0ms	2288×	body	80	nan
185.0ms	832×	body	320	valid
119.0ms	423×	body	160	valid
41.0ms	11×	body	5120	valid