Details

sample256.0ms

Algorithm

intervals

Results

99.0ms	89×	body	1280	valid
95.0ms	35×	body	2560	valid
21.0ms	46×	body	640	valid
8.0ms	33×	body	320	valid
6.0ms	86×	body	80	valid
4.0ms	73×	body	80	nan
1.0ms	7×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	414
1	25	414
2	59	414
3	140	414
4	347	414
5	1535	414
done	5000	414

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
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 → 281

Calls

4 calls:

383.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
183.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
23.0ms	(pow (+ 1.0 (/ i n)) n)
415.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

533.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
347.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
281.0ms	(pow (+ 1.0 (/ i n)) n)
486.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.0s

Counts

293 → 293

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	437	186805
1	1418	179104
done	5001	176377

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n)))
8.2b	(* (* 0.5 (log 1.0)) (* i i))
18.8b	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
93×	`add-sqr-sqrt`
83×	`*-un-lft-identity` `add-cube-cbrt`
48×	`associate-r`
35×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-/r*`
12×	`pow-prod-down`
9×	`div-inv`
6×	`cbrt-undiv` `div-exp`
5×	`associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`-commutative` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `flip-+`

Counts

4 → 180

Calls

4 calls:

14.0ms	(* (* i i) 0.5)
682.0ms	(* 100.0 (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n)))
42.0ms	(* (* 0.5 (log 1.0)) (* i i))
886.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n))

series779.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* i i) 0.5)
275.0ms	(* 100.0 (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n)))
184.0ms	(* (* 0.5 (log 1.0)) (* i i))
278.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) (/ i n))

simplify1.9s

Counts

192 → 192

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	320	117783
1	971	112193
done	5001	110407

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n)
0.1b	(* 100.0 (* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n))
7.7b	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
8.2b	(* (* 0.5 (log 1.0)) (* i i))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt`
23×	`pow1`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
17×	`associate-l`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `flip-+`

Counts

4 → 105

Calls

4 calls:

621.0ms	(* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n)
500.0ms	(* 100.0 (* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n))
732.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
37.0ms	(* (* 0.5 (log 1.0)) (* i i))

series1.1s

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n)
541.0ms	(* 100.0 (* (/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i) n))
181.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
203.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify2.5s

Counts

117 → 117

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	199	64325
1	555	61382
2	3013	60741
done	5000	60741

prune618.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
7.7b	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
8.2b	(* (* 0.5 (log 1.0)) (* i i))

rewrite729.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`pow1`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`cbrt-prod`
4×	`add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `div-exp` `associate-r` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
697.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
25.0ms	(* (* 0.5 (log 1.0)) (* i i))

series880.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(cbrt n)
237.0ms	(cbrt n)
165.0ms	(/ (+ (* (log 1.0) n) (- (+ (* (* i i) 0.5) (* 1.0 i)) (* (* 0.5 (log 1.0)) (* i i)))) i)
203.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify1.7s

Counts

86 → 86

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	137	33382
1	348	31452
2	1868	31174
done	5000	30455

prune434.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.8b

regimes581.0ms

Accuracy

53.1% (10.7b remaining)

Error of 21.7b against oracle of 11.0b and baseline of 33.8b

bsearch299.0ms

Steps

Iters	Range		Point
9	3.0812599035097804e-09	7.830610238325062	4.039962480132393
9	-69051.06592837533	-4.7512835972832904e-05	-0.008529206764181105

simplify13.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	33	1308
1	49	1308
done	49	1308

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.7s	962×	body	2560	valid
2.3s	2469×	body	1280	valid
686.0ms	1584×	body	640	valid
270.0ms	3111×	body	80	valid
229.0ms	878×	body	320	valid
197.0ms	2251×	body	80	nan
63.0ms	451×	body	160	valid
42.0ms	11×	body	5120	valid