Details

sample298.0ms

Algorithm

intervals

Results

122.0ms	39×	body	2560	valid
97.0ms	75×	body	1280	valid
27.0ms	47×	body	640	valid
20.0ms	105×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	71×	body	80	nan
4.0ms	20×	body	160	valid

simplify1.9s

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: 45.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.0b	(- (pow (+ 1 (/ i n)) n) 1)
7.9b	(pow (+ 1 (/ i n)) n)
12.6b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite1.2s

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:

502.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
195.0ms	(- (pow (+ 1 (/ i n)) n) 1)
33.0ms	(pow (+ 1 (/ i n)) n)
449.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

414.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
321.0ms	(- (pow (+ 1 (/ i n)) n) 1)
327.0ms	(pow (+ 1 (/ i n)) n)
356.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.8s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	1702
0	542

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.2b	(* 1/6 (* i (* i i)))
6.3b	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
20.7b	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

rewrite706.0ms

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))
43.0ms	(* 1/6 (* i (* i i)))
154.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
479.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

series229.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* i (* i i))
54.0ms	(* 1/6 (* i (* i i)))
49.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
77.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

simplify2.0s

Counts

146 → 146

Iterations

Iter	Nodes
done	5005
2	2329
1	627
0	238

prune896.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
0.2b	(* (* i i) 1/6)
3.3b	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
6.9b	(* (* (* i i) 1/6) n)

rewrite508.0ms

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:

273.0ms	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
32.0ms	(* (* i i) 1/6)
97.0ms	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
104.0ms	(* (* (* i i) 1/6) n)

series155.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 100 (+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2)))))
40.0ms	(* (* i i) 1/6)
42.0ms	(+ (* (* (* i i) 1/6) n) (+ n (* i (* n 1/2))))
29.0ms	(* (* (* i i) 1/6) n)

simplify1.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5005
2	1805
1	398
0	136

prune481.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 11.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
0.1b	(* i (* i 1/6))
0.3b	(* i 1/6)
2.2b	(* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i)))

rewrite524.0ms

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:

196.0ms	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
16.0ms	(* i (* i 1/6))
7.0ms	(* i 1/6)
301.0ms	(* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* 100 (* n (+ (+ (* i (* i 1/6)) 1) (* 1/2 i))))
31.0ms	(* i (* i 1/6))
16.0ms	(* i 1/6)
66.0ms	(* 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

prune629.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.1b

regimes332.0ms

Accuracy

56.5% (9.9b remaining)

Error of 20.3b against oracle of 10.4b and baseline of 33.1b

bsearch237.0ms

Steps

Iters	Range		Point
10	1.1508784487870086e-137	2.644987615850002e-119	1.4389956636303172e-137
10	-524937.0299516014	-3.8822111449762154e-05	-0.6272769565773454

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	20

end0.0ms

sample7.5s

Algorithm

intervals

Results

2.7s	2496×	body	1280	valid
2.6s	999×	body	2560	valid
871.0ms	1571×	body	640	valid
518.0ms	2226×	body	80	nan
249.0ms	3075×	body	80	valid
239.0ms	859×	body	320	valid
108.0ms	417×	body	160	valid
33.0ms	7×	body	5120	valid