Details

sample211.0ms

Algorithm

intervals

Results

97.0ms	95×	body	1280	valid
46.0ms	22×	body	2560	valid
31.0ms	59×	body	640	valid
6.0ms	27×	body	320	valid
6.0ms	90×	body	80	valid
4.0ms	80×	body	80	nan
2.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
6	3302
5	836
4	309
3	135
2	59
1	25
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.0b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite964.0ms

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:

377.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
222.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms	(pow (+ 1.0 (/ i n)) n)
312.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

460.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
266.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
239.0ms	(pow (+ 1.0 (/ i n)) n)
412.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify3.2s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
2	4676
1	1390
0	437

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.0b	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
10.4b	(* (log 1.0) (* (* i i) 0.5))
15.8b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite572.0ms

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:

23.0ms	(* (* i i) 0.5)
260.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
48.0ms	(* (log 1.0) (* (* i i) 0.5))
227.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series828.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* i i) 0.5)
284.0ms	(* 100.0 (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
260.0ms	(* (log 1.0) (* (* i i) 0.5))
243.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify2.6s

Counts

223 → 223

Iterations

Iter	Nodes
done	5001
2	4041
1	1013
0	333

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
1.8b	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
10.4b	(* (log 1.0) (* (* i i) 0.5))
11.1b	(* (/ 100.0 i) (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
160×	`*-un-lft-identity`
133×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
62×	`add-exp-log`
61×	`associate-r`
44×	`add-cbrt-cube`
27×	`distribute-lft-out`
23×	`div-exp`
21×	`pow1`
19×	`prod-exp`
18×	`associate-l`
15×	`cbrt-unprod`
13×	`associate-/r*`
12×	`cbrt-undiv` `div-inv`
10×	`pow-prod-down`
9×	`unswap-sqr`
6×	`associate-/l/`
4×	`frac-add` `associate-/l*` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `*-commutative` `flip-+`
2×	`flip3--` `associate-/r/` `flip--`
1×	`frac-times` `clear-num` `associate-+r-` `frac-2neg` `div-sub` `associate-l/` `associate-r/` `log-pow`

Counts

4 → 240

Calls

4 calls:

14.0ms	(* (* i i) 0.5)
180.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
65.0ms	(* (log 1.0) (* (* i i) 0.5))
217.0ms	(* (/ 100.0 i) (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* i i) 0.5)
152.0ms	(/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
175.0ms	(* (log 1.0) (* (* i i) 0.5))
221.0ms	(* (/ 100.0 i) (/ (+ (+ (* n (log 1.0)) (* 1.0 i)) (- (* (* i i) 0.5) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

simplify2.2s

Counts

252 → 252

Iterations

Iter	Nodes
done	5022
2	4523
1	1237
0	372

prune987.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ 1.0 (* 0.5 i)))
0.0b	(* 100.0 (/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i))
1.7b	(* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n)
10.9b	(/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

12.0ms	(* i (+ 1.0 (* 0.5 i)))
53.0ms	(* 100.0 (/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i))
66.0ms	(* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n)
23.0ms	(/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i)

series603.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* i (+ 1.0 (* 0.5 i)))
205.0ms	(* 100.0 (/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i))
146.0ms	(* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n)
186.0ms	(/ (* (+ (* n (log 1.0)) (- (* i (+ 1.0 (* 0.5 i))) (* (* (log 1.0) i) (* 0.5 i)))) n) i)

simplify1.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5019
2	2325
1	572
0	188

prune429.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.6b

regimes544.0ms

Accuracy

48.8% (11.1b remaining)

Error of 22.3b against oracle of 11.2b and baseline of 32.9b

bsearch251.0ms

Steps

Iters	Range		Point
7	4.3349714367632944e-150	5.208151982490766e-148	5.492513693153941e-150
6	-1.0692274826172779e-302	-7.189279918874739e-304	-2.7304039749009327e-303
7	-25254222.655854985	-733100.9210806559	-743560.0364592294

simplify14.0ms

Iterations

Iter	Nodes
done	66
1	66
0	47

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.0s	2501×	body	1280	valid
1.9s	947×	body	2560	valid
612.0ms	1605×	body	640	valid
523.0ms	3080×	body	80	valid
200.0ms	854×	body	320	valid
86.0ms	2179×	body	80	nan
53.0ms	443×	body	160	valid
37.0ms	9×	body	5120	valid