Details

sample270.0ms

Algorithm

intervals

Results

105.0ms	75×	body	1280	valid
82.0ms	24×	body	2560	valid
34.0ms	51×	body	640	valid
13.0ms	105×	body	80	valid
11.0ms	24×	body	320	valid
8.0ms	69×	body	80	nan
3.0ms	12×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	7318
5	1480
4	419
3	148
2	56
1	26
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize31.0ms

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))

rewrite562.0ms

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:

191.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
116.0ms	(- (pow (+ 1 (/ i n)) n) 1)
14.0ms	(pow (+ 1 (/ i n)) n)
231.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

377.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
333.0ms	(- (pow (+ 1 (/ i n)) n) 1)
309.0ms	(pow (+ 1 (/ i n)) n)
302.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify11.4s

Counts

465 → 465

Iterations

Iter	Nodes
2	5274
1	1671
0	542

prune3.9s

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)

rewrite385.0ms

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:

138.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
149.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
76.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

542.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
320.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
229.0ms	(- (pow (+ 1 (/ i n)) n) 1)
224.0ms	(pow (+ 1 (/ i n)) n)

simplify23.3s

Counts

494 → 494

Iterations

Iter	Nodes
2	4873
1	1958
0	565

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* i (* i i)) 1/6)
2.5b	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
8.1b	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
11.5b	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
159×	`*-un-lft-identity`
131×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
60×	`associate-r`
57×	`add-exp-log`
39×	`add-cbrt-cube`
27×	`distribute-lft-out`
23×	`div-exp`
16×	`prod-exp`
15×	`pow1`
14×	`associate-l`
13×	`associate-/r*`
12×	`cbrt-undiv` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
7×	`pow-prod-down`
6×	`add-log-exp`
4×	`insert-posit16` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 230

Calls

4 calls:

33.0ms	(* (* i (* i i)) 1/6)
136.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
14.0ms	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
143.0ms	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* i (* i i)) 1/6)
46.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
96.0ms	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
69.0ms	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

simplify2.8s

Counts

242 → 242

Iterations

Iter	Nodes
2	3748
1	1098
0	347

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* n (+ 100 (* 50 i)))
0.3b	(* (* (* i i) n) 50/3)
4.3b	(+ (* (* (* i i) n) 50/3) (* n (+ 100 (* 50 i))))
8.6b	(* (* i i) n)

rewrite99.0ms

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`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
4×	`insert-posit16`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 79

Calls

4 calls:

10.0ms	(* n (+ 100 (* 50 i)))
37.0ms	(* (* (* i i) n) 50/3)
37.0ms	(+ (* (* (* i i) n) 50/3) (* n (+ 100 (* 50 i))))
13.0ms	(* (* i i) n)

series122.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* n (+ 100 (* 50 i)))
22.0ms	(* (* (* i i) n) 50/3)
34.0ms	(+ (* (* (* i i) n) 50/3) (* n (+ 100 (* 50 i))))
19.0ms	(* (* i i) n)

simplify2.6s

Counts

91 → 91

Iterations

Iter	Nodes
3	7239
2	1503
1	386
0	128

prune505.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

regimes425.0ms

Accuracy

46.9% (12.1b remaining)

Error of 22.6b against oracle of 10.6b and baseline of 33.3b

bsearch275.0ms

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

simplify5.0ms

Iterations

Iter	Nodes
2	38
1	38
0	30

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	2490×	body	1280	valid
2.0s	953×	body	2560	valid
770.0ms	1574×	body	640	valid
281.0ms	3068×	body	80	valid
233.0ms	831×	body	320	valid
190.0ms	2254×	body	80	nan
112.0ms	450×	body	160	valid
32.0ms	8×	body	5120	valid