Details

sample237.0ms

Algorithm

intervals

Results

97.0ms	75×	body	1280	valid
67.0ms	24×	body	2560	valid
30.0ms	51×	body	640	valid
12.0ms	105×	body	80	valid
8.0ms	24×	body	320	valid
6.0ms	69×	body	80	nan
3.0ms	12×	body	160	valid

simplify742.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
7.4b	(pow (+ 1 (/ i n)) n)
8.4b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite479.0ms

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:

177.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
91.0ms	(- (pow (+ 1 (/ i n)) n) 1)
12.0ms	(pow (+ 1 (/ i n)) n)
174.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

379.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
249.0ms	(- (pow (+ 1 (/ i n)) n) 1)
248.0ms	(pow (+ 1 (/ i n)) n)
376.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.4s

Counts

465 → 465

Iterations

Iter	Nodes
done	2001
2	2001
1	1702
0	542

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
0.3b	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
7.4b	(pow (+ 1 (/ i n)) n)

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

604×	`times-frac`
510×	`add-sqr-sqrt`
374×	`*-un-lft-identity`
230×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
49×	`add-exp-log`
30×	`add-cbrt-cube` `div-inv`
28×	`distribute-lft-out--`
23×	`div-exp`
13×	`associate-/r` `associate-l` `associate-/l`
12×	`cbrt-undiv`
10×	`prod-exp`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`rec-exp` `pow-unpow` `1-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`frac-times` `pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `pow-exp` `associate-r/` `*-commutative` `distribute-lft-out`

Counts

4 → 482

Calls

4 calls:

178.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
235.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
97.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)

series1.4s

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
449.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
278.0ms	(- (pow (+ 1 (/ i n)) n) 1)
317.0ms	(pow (+ 1 (/ i n)) n)

simplify1.4s

Counts

494 → 494

Iterations

Iter	Nodes
done	2004
2	2004
1	1996
0	565

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* i (* i i)) 1/6)
2.5b	(/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n))
8.0b	(+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6))
11.5b	(* (/ 100 i) (/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
117×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
89×	`add-cube-cbrt`
57×	`add-exp-log`
47×	`associate-r`
39×	`add-cbrt-cube`
23×	`div-exp`
16×	`prod-exp`
15×	`pow1`
14×	`associate-l`
13×	`associate-/r*`
12×	`cbrt-undiv` `cbrt-unprod`
10×	`div-inv`
9×	`add-log-exp`
8×	`unswap-sqr`
7×	`pow-prod-down`
4×	`insert-posit16`
3×	`rec-exp` `sum-log` `1-exp` `associate-/l*`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`frac-times` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 205

Calls

4 calls:

44.0ms	(* (* i (* i i)) 1/6)
72.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n))
28.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6))
49.0ms	(* (/ 100 i) (/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* i (* i i)) 1/6)
51.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n))
28.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6))
77.0ms	(* (/ 100 i) (/ (+ (+ i (* (* i i) 1/2)) (* (* i (* i i)) 1/6)) (/ 1 n)))

simplify963.0ms

Counts

217 → 217

Iterations

Iter	Nodes
done	2001
2	2001
1	1071
0	343

prune2.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 50 (* i n))
0.3b	(* 50/3 (* n (* i i)))
4.3b	(+ (* 50/3 (* n (* i i))) (* 50 (* i n)))
8.6b	(* n (* i i))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

14.0ms	(* 50 (* i n))
37.0ms	(* 50/3 (* n (* i i)))
36.0ms	(+ (* 50/3 (* n (* i i))) (* 50 (* i n)))
14.0ms	(* n (* i i))

series197.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 50 (* i n))
43.0ms	(* 50/3 (* n (* i i)))
87.0ms	(+ (* 50/3 (* n (* i i))) (* 50 (* i n)))
39.0ms	(* n (* i i))

simplify971.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2023
3	2023
2	1119
1	302
0	108

prune563.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.3b

regimes265.0ms

Accuracy

46.6% (12.2b remaining)

Error of 22.7b against oracle of 10.5b and baseline of 33.3b

bsearch315.0ms

Steps

Iters	Range		Point
4	3.4102531824377107e-252	6.77630104842725e-252	6.641285833915873e-252
8	-8955.820626370843	-0.35383103211093586	-0.5086740071675135
8	-9.784393806346407e+114	-8.772610801518598e+111	-1.4608487543202562e+112

simplify7.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.1s	2490×	body	1280	valid
2.3s	953×	body	2560	valid
828.0ms	1574×	body	640	valid
376.0ms	3068×	body	80	valid
355.0ms	831×	body	320	valid
186.0ms	2254×	body	80	nan
113.0ms	450×	body	160	valid
35.0ms	8×	body	5120	valid