Details

sample254.0ms

Algorithm

intervals

Results

103.0ms	86×	body	1280	valid
66.0ms	25×	body	2560	valid
41.0ms	52×	body	640	valid
10.0ms	101×	body	80	valid
8.0ms	23×	body	320	valid
7.0ms	76×	body	80	nan
4.0ms	18×	body	160	valid

simplify817.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
5	2006
4	512
3	150
2	58
1	28
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
2.0b	(- (pow (+ 1 (/ i n)) n) 1)
5.6b	(pow (+ 1 (/ i n)) n)
8.0b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite431.0ms

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:

154.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
89.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
163.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

426.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
299.0ms	(- (pow (+ 1 (/ i n)) n) 1)
253.0ms	(pow (+ 1 (/ i n)) n)
375.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.3s

Counts

465 → 465

Iterations

Iter	Nodes
done	2001
2	2001
1	1702
0	542

prune4.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.3b	(* 1/6 (* i (* i i)))
6.5b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
14.4b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

19.0ms	(* i (* i i))
32.0ms	(* 1/6 (* i (* i i)))
18.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
185.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

series302.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* i (* i i))
41.0ms	(* 1/6 (* i (* i i)))
130.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
79.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

simplify918.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2001
2	2001
1	648
0	240

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (* i (* i i)))
2.1b	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
4.2b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
6.5b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-l`
15×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down` `distribute-lft-out`
6×	`add-log-exp`
4×	`associate-r` `insert-posit16` `associate-/l*`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `*-commutative` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-*l/`

Counts

4 → 104

Calls

4 calls:

32.0ms	(* 1/6 (* i (* i i)))
166.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
167.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
18.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/6 (* i (* i i)))
92.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
54.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
124.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

simplify1.2s

Counts

116 → 116

Iterations

Iter	Nodes
done	2005
3	2005
2	1636
1	456
0	169

prune905.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n))
0.1b	(* (* 1/6 i) i)
0.4b	(* 1/6 i)
2.1b	(* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n)

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

93.0ms	(* 100 (* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n))
13.0ms	(* (* 1/6 i) i)
5.0ms	(* 1/6 i)
109.0ms	(* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n)

series128.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 100 (* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n))
28.0ms	(* (* 1/6 i) i)
16.0ms	(* 1/6 i)
39.0ms	(* (+ (* i 1/2) (+ (* (* 1/6 i) i) 1)) n)

simplify872.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2009
3	2009
2	1265
1	360
0	129

prune573.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.1b

regimes216.0ms

Accuracy

54.2% (10.5b remaining)

Error of 21.3b against oracle of 10.9b and baseline of 33.7b

bsearch335.0ms

Steps

Iters	Range		Point
11	2.9348777329819658e-12	3.1891227468784625e+20	4.5457902375689345
9	-1.9696345359431407e-07	-4.750217372511675e-17	-1.9324505473046543e-07

simplify8.0ms

Iterations

Iter	Nodes
done	43
1	43
0	31

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.9s	2440×	body	1280	valid
2.3s	957×	body	2560	valid
940.0ms	1643×	body	640	valid
325.0ms	3092×	body	80	valid
281.0ms	877×	body	320	valid
242.0ms	2249×	body	80	nan
110.0ms	445×	body	160	valid
26.0ms	6×	body	5120	valid