Details

sample235.0ms

Algorithm

intervals

Results

94.0ms	89×	body	1280	valid
85.0ms	35×	body	2560	valid
19.0ms	46×	body	640	valid
9.0ms	33×	body	320	valid
6.0ms	86×	body	80	valid
4.0ms	73×	body	80	nan
1.0ms	7×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.8b

localize21.0ms

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)
5.3b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite900.0ms

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:

365.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
149.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms	(pow (+ 1.0 (/ i n)) n)
336.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

599.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
322.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
271.0ms	(pow (+ 1.0 (/ i n)) n)
478.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify696.0ms

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
8.2b	(* (log 1.0) (* (* i i) 0.5))
18.8b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite635.0ms

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:

14.0ms	(* (* i i) 0.5)
314.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
45.0ms	(* (log 1.0) (* (* i i) 0.5))
248.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series760.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* i i) 0.5)
258.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
218.0ms	(* (log 1.0) (* (* i i) 0.5))
231.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify648.0ms

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
1	1046
0	333

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n)
0.1b	(* 100.0 (* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n))
7.7b	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i)
8.2b	(* (log 1.0) (- n (* (* 0.5 i) i)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

33.0ms	(* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n)
51.0ms	(* 100.0 (* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n))
52.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i)
22.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

series947.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n)
272.0ms	(* 100.0 (* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i) n))
174.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) i)
265.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify1.7s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	3640
1	633
0	219

prune643.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
1.4b	(/ (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i)))) (/ (cbrt i) (cbrt n)))
5.2b	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i))))
8.2b	(* (log 1.0) (- n (* (* 0.5 i) i)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

35618×	`times-frac`
13335×	`cbrt-prod`
12759×	`add-sqr-sqrt`
12757×	`*-un-lft-identity` `add-cube-cbrt`
1133×	`div-inv`
203×	`associate-/l*`
170×	`associate-/r/`
105×	`associate-/r*`
65×	`add-exp-log`
42×	`cbrt-undiv` `div-exp`
34×	`add-cbrt-cube`
10×	`associate-*r/`
7×	`pow1` `associate-/l/`
4×	`associate-l` `frac-add` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip3--` `associate-r` `flip-+` `flip--`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in`
1×	`pow1/3` `pow-prod-down` `log-pow` `*-commutative` `unswap-sqr`

Counts

4 → 8596

Calls

4 calls:

1.0ms	(cbrt n)
294.0ms	(/ (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i)))) (/ (cbrt i) (cbrt n)))
56.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i))))
15.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt n)
250.0ms	(/ (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i)))) (/ (cbrt i) (cbrt n)))
192.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* (* 0.5 i) i)))) (/ (cbrt i) (/ (* (cbrt n) (cbrt n)) (cbrt i))))
217.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify4.0s

Counts

8608 → 8608

Iterations

Iter	Nodes
done	10978
0	10978

prune1.2m

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.7b

regimes298.0ms

Accuracy

53.8% (10.6b remaining)

Error of 21.5b against oracle of 10.9b and baseline of 33.8b

bsearch233.0ms

Steps

Iters	Range		Point
9	3.0812599035097804e-09	7.830610238325062	4.039962480132393
9	-69051.06592837533	-4.7512835972832904e-05	-0.008529206764181105

simplify9.0ms

Iterations

Iter	Nodes
done	53
3	53
2	51
1	49
0	35

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	962×	body	2560	valid
2.0s	2469×	body	1280	valid
563.0ms	1584×	body	640	valid
202.0ms	878×	body	320	valid
191.0ms	3111×	body	80	valid
122.0ms	2251×	body	80	nan
111.0ms	451×	body	160	valid
36.0ms	11×	body	5120	valid