Details

sample203.0ms

Algorithm

intervals

Results

74.0ms	79×	body	1280	valid
67.0ms	28×	body	2560	valid
24.0ms	54×	body	640	valid
8.0ms	32×	body	320	valid
6.0ms	99×	body	80	valid
3.0ms	58×	body	80	nan
2.0ms	13×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune9.0ms

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))

rewrite875.0ms

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:

324.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
195.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
325.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

461.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
317.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
273.0ms	(pow (+ 1.0 (/ i n)) n)
419.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.1s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* i i) 0.5) (* 1.0 i))
0.1b	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
8.9b	(* (log 1.0) (* (* i i) 0.5))
15.2b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 203

Calls

4 calls:

19.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
238.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
39.0ms	(* (log 1.0) (* (* i i) 0.5))
210.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series799.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
270.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
179.0ms	(* (log 1.0) (* (* i i) 0.5))
262.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify1.9s

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1064
0	336

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
0.0b	(* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) (* n 100.0))
8.4b	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
8.9b	(* (log 1.0) (- n (* i (* i 0.5))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
18×	`times-frac`
17×	`associate-l`
12×	`pow1`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `associate-/r` `sum-log` `div-exp` `associate-/l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `flip3--` `associate-*l/` `log-pow` `flip--` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

39.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
142.0ms	(* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) (* n 100.0))
95.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
19.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
288.0ms	(* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) (* n 100.0))
172.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
161.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	3103
1	556
0	192

prune691.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
0.1b	(* (* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i)) (* n 100.0))
8.6b	(* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i))
8.9b	(* (log 1.0) (- n (* i (* i 0.5))))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
32×	`add-cbrt-cube`
28×	`prod-exp`
23×	`add-sqr-sqrt`
21×	`pow1`
17×	`associate-r`
16×	`cbrt-unprod`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`times-frac`
10×	`pow-prod-down` `associate-*l/`
9×	`add-log-exp`
8×	`associate-l`
6×	`div-exp`
5×	`flip3-+` `flip-+`
4×	`frac-times` `associate-*r/` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `sum-log` `1-exp` `*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `un-div-inv`
1×	`+-commutative` `associate-+l+` `flip3--` `log-pow` `div-inv` `flip--`

Counts

4 → 114

Calls

4 calls:

45.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
159.0ms	(* (* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i)) (* n 100.0))
146.0ms	(* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i))
21.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
246.0ms	(* (* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i)) (* n 100.0))
174.0ms	(* (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) (/ 1 i))
206.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify4.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	4985
1	662
0	223

prune499.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

regimes234.0ms

Accuracy

42.1% (13.1b remaining)

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

bsearch323.0ms

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

simplify13.0ms

Iterations

Iter	Nodes
done	60
2	60
1	59
0	42

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.2s	2575×	body	1280	valid
1.9s	917×	body	2560	valid
634.0ms	1578×	body	640	valid
475.0ms	3075×	body	80	valid
208.0ms	879×	body	320	valid
182.0ms	2237×	body	80	nan
60.0ms	457×	body	160	valid
35.0ms	9×	body	5120	valid