Details

sample680.0ms

Algorithm

intervals

Results

355.0ms	101×	body	80	valid
140.0ms	95×	body	1280	valid
93.0ms	26×	body	2560	valid
34.0ms	48×	body	640	valid
13.0ms	26×	body	320	valid
10.0ms	80×	body	80	nan
8.0ms	2×	body	5120	valid
6.0ms	17×	body	160	valid

simplify608.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	512
3	150
2	58
1	28
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
0.3b	(- (pow (+ 1 (/ i n)) n) 1)
6.8b	(pow (+ 1 (/ i n)) n)
11.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite644.0ms

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:

243.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
129.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
245.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

433.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
298.0ms	(- (pow (+ 1 (/ i n)) n) 1)
292.0ms	(pow (+ 1 (/ i n)) n)
399.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.2s

Counts

465 → 465

Iterations

Iter	Nodes
done	2001
1	1702
0	542

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.1b	(* 1/6 (* i (* i i)))
5.3b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
18.7b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

rewrite271.0ms

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:

28.0ms	(* i (* i i))
41.0ms	(* 1/6 (* i (* i i)))
19.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
178.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

series350.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* i (* i i))
65.0ms	(* 1/6 (* i (* i i)))
118.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
101.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

simplify580.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2001
1	648
0	240

prune670.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* i (* i i)))
1.3b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n))
5.3b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
14.8b	(* (/ 1 i) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n)))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

217×	`times-frac`
164×	`*-un-lft-identity`
143×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`associate-r`
40×	`div-exp`
39×	`add-cbrt-cube`
27×	`distribute-lft-out`
26×	`prod-exp`
16×	`associate-l`
15×	`pow1`
13×	`associate-/r*`
12×	`cbrt-undiv` `cbrt-unprod` `div-inv` `unswap-sqr`
10×	`rec-exp` `1-exp`
7×	`pow-prod-down`
6×	`add-log-exp`
4×	`insert-posit16` `associate-/l*`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 244

Calls

4 calls:

47.0ms	(* 1/6 (* i (* i i)))
201.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n))
28.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
224.0ms	(* (/ 1 i) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* 1/6 (* i (* i i)))
67.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n))
129.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
90.0ms	(* (/ 1 i) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ 1 n)))

simplify663.0ms

Counts

256 → 256

Iterations

Iter	Nodes
done	2001
1	1131
0	350

prune992.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (/ 1 n))
1.1b	(* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n))))
5.3b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
14.8b	(* (/ 1 i) (* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n)))))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

308×	`add-exp-log`
160×	`prod-exp`
149×	`times-frac`
109×	`add-sqr-sqrt` `*-un-lft-identity`
105×	`div-exp`
74×	`cbrt-prod`
70×	`associate-r`
69×	`add-cbrt-cube` `add-cube-cbrt`
38×	`cbrt-unprod`
35×	`rec-exp` `1-exp`
28×	`cbrt-undiv`
23×	`associate-l`
16×	`distribute-lft-out`
15×	`unswap-sqr`
11×	`pow1`
8×	`div-inv`
7×	`frac-times` `associate-*r/`
6×	`cbrt-div` `add-log-exp`
5×	`associate-*l/`
4×	`pow-prod-down` `associate-/r/` `insert-posit16`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 268

Calls

4 calls:

1.0ms	(cbrt (/ 1 n))
211.0ms	(* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n))))
32.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
239.0ms	(* (/ 1 i) (* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n)))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt (/ 1 n))
124.0ms	(* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n))))
112.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
109.0ms	(* (/ 1 i) (* (/ 1 (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (cbrt (/ 1 n)))))

simplify1.1s

Counts

280 → 280

Iterations

Iter	Nodes
done	2003
1	1324
0	423

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.4b

regimes412.0ms

Accuracy

53.9% (10.2b remaining)

Error of 21.0b against oracle of 10.8b and baseline of 33.0b

bsearch779.0ms

Steps

Iters	Range		Point
5	1.028088151699927e+297	2.1345817878143117e+297	1.1905568301770126e+297
8	7.041325302301213e+252	7.326822544245665e+255	7.515275266640414e+254
9	0.5242927222148749	19453700.538560145	44.79644908506854
7	2.8299509055291887e-239	6.805979708043197e-237	8.143655347585655e-238
9	-1.2862858880804409e-14	-2.4564544670811215e-20	-1.1676448974447302e-14

simplify29.0ms

Iterations

Iter	Nodes
done	76
1	76
0	56

end0.0ms

sample9.1s

Algorithm

intervals

Results

3.9s	2542×	body	1280	valid
2.6s	948×	body	2560	valid
1.0s	1614×	body	640	valid
391.0ms	3023×	body	80	valid
378.0ms	854×	body	320	valid
258.0ms	2178×	body	80	nan
158.0ms	440×	body	160	valid
64.0ms	14×	body	5120	valid