Details

sample199.0ms

Algorithm

intervals

Results

77.0ms	87×	body	1280	valid
59.0ms	24×	body	2560	valid
21.0ms	52×	body	640	valid
7.0ms	32×	body	320	valid
6.0ms	93×	body	80	valid
4.0ms	80×	body	80	nan
3.0ms	19×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
6	3302
5	836
4	309
3	135
2	59
1	25
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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:

471.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms	(pow (+ 1.0 (/ i n)) n)
308.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

567.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
351.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
333.0ms	(pow (+ 1.0 (/ i n)) n)
592.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify3.4s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
2	4676
1	1390
0	437

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5))))
0.1b	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
12.1b	(* (log 1.0) (* (* i i) 0.5))
18.2b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
153×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
97×	`add-cube-cbrt`
58×	`associate-r`
28×	`distribute-lft-out`
27×	`add-cbrt-cube` `add-exp-log`
16×	`pow1` `add-log-exp`
13×	`associate-/r*`
11×	`div-inv`
9×	`prod-exp` `cbrt-unprod`
8×	`frac-add`
7×	`associate-l` `pow-prod-down`
6×	`cbrt-undiv` `sum-log` `flip3-+` `div-exp` `flip-+` `associate-/l/`
4×	`flip3--` `flip--` `associate-/l*`
3×	`unswap-sqr`
2×	`associate-+r+` `associate-+r-` `diff-log` `associate-/r/` `*-commutative`
1×	`+-commutative` `associate-+l+` `clear-num` `sub-neg` `frac-2neg` `div-sub` `associate-*r/` `log-pow`

Counts

4 → 215

Calls

4 calls:

71.0ms	(+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5))))
227.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
48.0ms	(* (log 1.0) (* (* i i) 0.5))
214.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series828.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5))))
256.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
208.0ms	(* (log 1.0) (* (* i i) 0.5))
214.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify2.9s

Counts

227 → 227

Iterations

Iter	Nodes
done	5003
2	4878
1	1132
0	363

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i))
0.1b	(* (* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)) n)
11.5b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)
12.1b	(* (log 1.0) (* (* i i) 0.5))

rewrite679.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
25×	`times-frac`
24×	`add-cube-cbrt`
21×	`pow1`
20×	`associate-r`
13×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
8×	`associate-l`
7×	`distribute-lft-out`
6×	`associate-/l/`
4×	`frac-add` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `flip3-+` `div-exp` `-commutative` `flip-+`
2×	`flip3--` `associate-*r/` `div-inv` `flip--` `unswap-sqr`
1×	`clear-num` `associate-+r-` `frac-2neg` `div-sub` `associate-*l/` `log-pow`

Counts

4 → 116

Calls

4 calls:

215.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i))
239.0ms	(* (* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)) n)
177.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)
45.0ms	(* (log 1.0) (* (* i i) 0.5))

series807.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i))
240.0ms	(* (* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)) n)
166.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)
177.0ms	(* (log 1.0) (* (* i i) 0.5))

simplify1.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2727
1	650
0	218

prune526.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.0b

localize52.0ms

Local error

Found 4 expressions with local error:

12.1b	(* (log 1.0) (* (* i i) 0.5))
12.2b	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
12.2b	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
12.2b	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
14×	`pow1` `*-un-lft-identity`
13×	`add-cbrt-cube` `add-exp-log`
12×	`cbrt-prod` `frac-add`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
4×	`associate-l` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
1×	`associate-r` `log-pow` `*-commutative`

Counts

4 → 76

Calls

4 calls:

40.0ms	(* (log 1.0) (* (* i i) 0.5))
65.0ms	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
57.0ms	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
51.0ms	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))

series8.7s

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (log 1.0) (* (* i i) 0.5))
3.1s	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
2.7s	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))
2.7s	(cbrt (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))))

simplify1.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1906
1	473
0	157

prune570.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.0b

regimes269.0ms

Accuracy

52.6% (10.8b remaining)

Error of 22.2b against oracle of 11.4b and baseline of 34.2b

bsearch289.0ms

Steps

Iters	Range		Point
7	7.2949686944817395e+205	1.8280591761267005e+208	1.540498293983816e+208
12	9.084828359643272e-19	1.6311032011848909e+25	1.9432388931584246
5	-7.642915086960539e-08	-3.0023583529873386e-08	-7.524185979796087e-08

simplify16.0ms

Iterations

Iter	Nodes
done	73
1	73
0	53

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	2441×	body	1280	valid
1.8s	972×	body	2560	valid
604.0ms	1619×	body	640	valid
221.0ms	920×	body	320	valid
160.0ms	3005×	body	80	valid
136.0ms	2297×	body	80	nan
76.0ms	453×	body	160	valid
31.0ms	9×	body	5120	valid