Details

sample224.0ms

Algorithm

intervals

Results

91.0ms	79×	body	1280	valid
67.0ms	28×	body	2560	valid
23.0ms	54×	body	640	valid
7.0ms	32×	body	320	valid
7.0ms	99×	body	80	valid
3.0ms	58×	body	80	nan
2.0ms	13×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

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)
4.9b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite955.0ms

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:

398.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
175.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
24.0ms	(pow (+ 1.0 (/ i n)) n)
330.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

486.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
333.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
286.0ms	(pow (+ 1.0 (/ i n)) n)
515.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify3.1s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
2	4676
1	1390
0	437

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 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)))
8.9b	(* (log 1.0) (* (* i i) 0.5))
15.2b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite506.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
152×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
61×	`associate-r`
32×	`add-cbrt-cube` `add-exp-log`
27×	`distribute-lft-out`
21×	`pow1`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`div-inv`
10×	`pow-prod-down`
8×	`associate-l`
6×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`frac-add` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`flip3--` `associate-/r/` `flip--`
1×	`clear-num` `associate-+r-` `frac-2neg` `div-sub` `associate-*r/` `log-pow`

Counts

4 → 211

Calls

4 calls:

15.0ms	(* (* i i) 0.5)
235.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
55.0ms	(* (log 1.0) (* (* i i) 0.5))
191.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series672.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* i i) 0.5)
231.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
206.0ms	(* (log 1.0) (* (* i i) 0.5))
204.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify2.1s

Counts

223 → 223

Iterations

Iter	Nodes
done	5001
2	4041
1	1013
0	333

prune976.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.4b

localize35.0ms

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)
8.4b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)
8.9b	(* (log 1.0) (* (* i i) 0.5))

rewrite556.0ms

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:

175.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i))
191.0ms	(* (* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)) n)
148.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)
39.0ms	(* (log 1.0) (* (* i i) 0.5))

series693.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i))
202.0ms	(* (* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) i)) n)
148.0ms	(/ (+ (+ (* 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))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2727
1	650
0	218

prune548.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.4b

localize45.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (log 1.0) (* (* i i) 0.5))
14.1b	(cbrt (/ i n))
14.1b	(cbrt (/ i n))
14.1b	(cbrt (/ i n))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-l` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`associate-r` `log-pow` `*-commutative`

Counts

4 → 88

Calls

4 calls:

44.0ms	(* (log 1.0) (* (* i i) 0.5))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))

series365.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (log 1.0) (* (* i i) 0.5))
63.0ms	(cbrt (/ i n))
67.0ms	(cbrt (/ i n))
66.0ms	(cbrt (/ i n))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5003
3	3276
2	701
1	251
0	123

prune750.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 10.4b

regimes237.0ms

Accuracy

42.1% (13.1b remaining)

Error of 24.3b against oracle of 11.2b and baseline of 33.8b

bsearch308.0ms

Steps

Iters	Range		Point
10	-8.507001710182289e-307	8.575654121239942e-297	8.43948162108991e-297
5	-2.085807323628561e+25	-8.665460962243007e+24	-1.5240705750258725e+25
8	-1.3111623360014479e+36	-4.953784207856335e+31	-4.995965210525052e+35
6	-4.468344328437476e+60	-4.544149282436552e+59	-5.46477309603401e+59

simplify11.0ms

Iterations

Iter	Nodes
done	55
1	55
0	40

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	2575×	body	1280	valid
2.0s	917×	body	2560	valid
1.0s	1578×	body	640	valid
277.0ms	3075×	body	80	valid
245.0ms	879×	body	320	valid
129.0ms	2237×	body	80	nan
62.0ms	457×	body	160	valid
40.0ms	9×	body	5120	valid