Details

sample209.0ms

Algorithm

intervals

Results

82.0ms	87×	body	1280	valid
59.0ms	24×	body	2560	valid
23.0ms	52×	body	640	valid
14.0ms	32×	body	320	valid
6.0ms	93×	body	80	valid
4.0ms	80×	body	80	nan
3.0ms	19×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune10.0ms

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:

456.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
184.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms	(pow (+ 1.0 (/ i n)) n)
438.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

535.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
351.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
329.0ms	(pow (+ 1.0 (/ i n)) n)
538.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.3s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.3b

localize33.0ms

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

rewrite554.0ms

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:

28.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
235.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
40.0ms	(* (log 1.0) (* (* i i) 0.5))
234.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series872.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
254.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
282.0ms	(* (log 1.0) (* (* i i) 0.5))
243.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify1.7s

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1064
0	336

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize32.0ms

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

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

46.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
103.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) n))
98.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
18.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i))
305.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) n))
176.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
211.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2724
1	506
0	186

prune455.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`cbrt-div` `add-cbrt-cube` `add-exp-log`
4×	`associate-l` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-r` `flip-+`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
21.0ms	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))
25.0ms	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))
22.0ms	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))

series8.4s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
2.6s	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))
3.0s	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))
2.5s	(cbrt (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)))

simplify1.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1371
1	304
0	117

prune456.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

regimes248.0ms

Accuracy

52.6% (10.8b remaining)

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

bsearch346.0ms

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

simplify19.0ms

Iterations

Iter	Nodes
done	77
2	77
1	74
0	52

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.2s	972×	body	2560	valid
2.1s	2441×	body	1280	valid
691.0ms	1619×	body	640	valid
246.0ms	920×	body	320	valid
192.0ms	3005×	body	80	valid
120.0ms	2297×	body	80	nan
58.0ms	453×	body	160	valid
34.0ms	9×	body	5120	valid