Details

sample249.0ms

Algorithm

intervals

Results

100.0ms	35×	body	2560	valid
74.0ms	76×	body	1280	valid
27.0ms	53×	body	640	valid
8.0ms	25×	body	320	valid
8.0ms	96×	body	80	valid
6.0ms	90×	body	80	nan
3.0ms	15×	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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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:

485.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
205.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(pow (+ 1.0 (/ i n)) n)
435.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

509.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
365.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
319.0ms	(pow (+ 1.0 (/ i n)) n)
555.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify763.0ms

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize48.0ms

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)))
10.4b	(* (log 1.0) (* (* i i) 0.5))
17.2b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite756.0ms

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:

16.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
344.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
75.0ms	(* (log 1.0) (* (* i i) 0.5))
310.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series927.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
314.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
250.0ms	(* (log 1.0) (* (* i i) 0.5))
280.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify589.0ms

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1064
0	336

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize51.0ms

Local error

Found 4 expressions with local error:

10.4b	(* (log 1.0) (- n (* i (* i 0.5))))
10.5b	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
10.5b	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
10.5b	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
13.0ms	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
29.0ms	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
21.0ms	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))

series3.5s

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
1.1s	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
1.0s	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))
1.1s	(cbrt (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2482
1	506
0	171

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0)
0.5b	(* (/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i) n)
9.5b	(/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i)
10.4b	(* (log 1.0) (- n (* i (* i 0.5))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

62.0ms	(* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0)
63.0ms	(* (/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i) n)
53.0ms	(/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i)
15.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series982.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0)
319.0ms	(* (/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i) n)
254.0ms	(/ (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) 100.0) i)
225.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify2.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	4714
1	722
0	232

prune605.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 11.4b

regimes377.0ms

Accuracy

43.6% (12.6b remaining)

Error of 23.6b against oracle of 10.9b and baseline of 33.3b

bsearch465.0ms

Steps

Iters	Range		Point
7	1.2245728681896357e-155	1.2152850197652755e-153	1.4183297845116364e-154
7	-22.8286883066892	-0.10952899301968014	-1.8594290872480363
8	-8.389936357340607e+106	-5.720382841890011e+103	-8.23875326441092e+106
7	-4.1468841507459867e+123	-2.615624459402513e+121	-6.142887410522618e+122

simplify24.0ms

Iterations

Iter	Nodes
done	74
1	74
0	53

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	995×	body	2560	valid
2.0s	2450×	body	1280	valid
594.0ms	1640×	body	640	valid
362.0ms	454×	body	160	valid
253.0ms	3041×	body	80	valid
162.0ms	835×	body	320	valid
92.0ms	2189×	body	80	nan
24.0ms	7×	body	5120	valid