Details

sample297.0ms

Algorithm

intervals

Results

121.0ms	35×	body	2560	valid
105.0ms	77×	body	1280	valid
23.0ms	43×	body	640	valid
9.0ms	31×	body	320	valid
7.0ms	85×	body	80	valid
4.0ms	63×	body	80	nan
3.0ms	16×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	140	15
4	347	15
5	1514	15
done	5000	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.5b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

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` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

545.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
200.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms	(pow (+ 1.0 (/ i n)) n)
535.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

500.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
357.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
304.0ms	(pow (+ 1.0 (/ i n)) n)
522.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify921.0ms

Counts

293 → 293

Iterations

Useful iterations: done (908.0ms)

Iter	Nodes	Cost
0	437	6469
1	1416	6211
done	5000	5919

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.1b	(* (pow i 2) (log 1.0))
20.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite875.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

21.0ms	(* 0.5 (pow i 2))
377.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
27.0ms	(* (pow i 2) (log 1.0))
433.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 0.5 (pow i 2))
288.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
549.0ms	(* (pow i 2) (log 1.0))
247.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify606.0ms

Counts

212 → 212

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	345	6722
1	1016	6538
done	5000	6030

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
2.8b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
12.1b	(* (pow i 2) (log 1.0))
12.7b	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite712.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
136×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
96×	`add-cube-cbrt`
58×	`add-exp-log`
56×	`associate-r`
34×	`add-cbrt-cube`
24×	`associate-l`
23×	`div-exp`
16×	`prod-exp` `unswap-sqr`
13×	`associate-/r*`
12×	`cbrt-undiv`
10×	`div-inv`
8×	`unpow-prod-down` `cbrt-unprod`
7×	`pow1`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `flip--`

Counts

4 → 229

Calls

4 calls:

22.0ms	(* 0.5 (pow i 2))
314.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
19.0ms	(* (pow i 2) (log 1.0))
342.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 0.5 (pow i 2))
176.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
204.0ms	(* (pow i 2) (log 1.0))
248.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify674.0ms

Counts

241 → 241

Iterations

Useful iterations: done (663.0ms)

Iter	Nodes	Cost
0	387	8200
1	1245	7797
done	5001	6871

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.1b	(* (pow i 2) (log 1.0))

rewrite646.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-r`
11×	`prod-exp`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

13.0ms	(* 0.5 (pow i 2))
271.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
331.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
27.0ms	(* (pow i 2) (log 1.0))

series675.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* 0.5 (pow i 2))
250.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
187.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
205.0ms	(* (pow i 2) (log 1.0))

simplify1.6s

Counts

124 → 124

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	216	2789
1	534	2708
2	2675	2302
done	5001	2300

prune452.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 11.7b

regimes264.0ms

Accuracy

52.2% (10.6b remaining)

Error of 21.6b against oracle of 11.0b and baseline of 33.2b

bsearch436.0ms

Steps

Iters	Range		Point
8	5.344653673325432e+100	5.6044378618353505e+103	5.534188978290048e+103
10	0.00038500758258708294	1371021975238077.5	1.1647242678127252
9	-13.304859898696009	-9.641814872486784e-07	-0.0035428999671728045

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	107
1	69	107
done	69	107

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	936×	body	2560	valid
2.1s	2478×	body	1280	valid
654.0ms	1611×	body	640	valid
389.0ms	465×	body	160	valid
219.0ms	902×	body	320	valid
175.0ms	3090×	body	80	valid
102.0ms	2341×	body	80	nan
21.0ms	5×	body	5120	valid