Details

sample213.0ms

Algorithm

intervals

Results

81.0ms	89×	body	1280	valid
77.0ms	35×	body	2560	valid
18.0ms	46×	body	640	valid
7.0ms	33×	body	320	valid
5.0ms	86×	body	80	valid
3.0ms	73×	body	80	nan
1.0ms	7×	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: 45.9b

localize27.0ms

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))

rewrite1.0s

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:

457.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
188.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
328.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

546.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
396.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
268.0ms	(pow (+ 1.0 (/ i n)) n)
519.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.1s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize62.0ms

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))

rewrite618.0ms

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)
273.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
38.0ms	(* (log 1.0) (* (* i i) 0.5))
281.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series844.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* i i) 0.5)
323.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
254.0ms	(* (log 1.0) (* (* i i) 0.5))
236.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify1.5s

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
1	1046
0	333

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.8b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite417.0ms

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`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r/` `-commutative` `associate-/l` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `log-pow` `flip-+` `flip--`

Counts

4 → 107

Calls

4 calls:

129.0ms	(* (/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i) n)
134.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i) n))
126.0ms	(/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i)
21.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i) n)
220.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i) n))
165.0ms	(/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i)
187.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify2.2s

Counts

119 → 119

Iterations

Iter	Nodes
done	5004
2	2995
1	559
0	201

prune684.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
7.7b	(/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i)
8.2b	(* (log 1.0) (- n (* (* 0.5 i) i)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
103.0ms	(/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i)
14.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt n)
257.0ms	(cbrt n)
150.0ms	(/ (+ (+ (* (log 1.0) (- n (* (* 0.5 i) i))) (* (* 0.5 i) i)) (* 1.0 i)) i)
192.0ms	(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1677
1	345
0	140

prune608.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.8b

regimes564.0ms

Accuracy

53.1% (10.7b remaining)

Error of 21.7b against oracle of 11.0b and baseline of 33.8b

bsearch310.0ms

Steps

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

simplify17.0ms

Iterations

Iter	Nodes
done	46
1	46
0	31

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2469×	body	1280	valid
2.1s	962×	body	2560	valid
1.0s	1584×	body	640	valid
185.0ms	878×	body	320	valid
174.0ms	2251×	body	80	nan
174.0ms	3111×	body	80	valid
116.0ms	451×	body	160	valid
38.0ms	11×	body	5120	valid