Details

sample138.0ms

Algorithm

intervals

Results

55.0ms	29×	body	2560	valid
44.0ms	66×	body	1280	valid
14.0ms	49×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	98×	body	80	valid
2.0ms	20×	body	160	valid
2.0ms	58×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	58	15
3	137	15
4	325	15
5	984	15
6	3830	15
done	5000	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
8.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite635.0ms

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` `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:

257.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
119.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms	(pow (+ 1.0 (/ i n)) n)
227.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

378.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
261.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
227.0ms	(pow (+ 1.0 (/ i n)) n)
373.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.4s

Counts

293 → 293

Iterations

Useful iterations: 2 (771.0ms)

Iter	Nodes	Cost
0	437	6469
1	1221	6125
2	3783	5875
done	5001	5875

prune874.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
2.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
8.7b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`times-frac`
28×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r*`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `unpow-prod-down` `div-exp` `add-log-exp` `difference-of-squares`
4×	`associate-*r/`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

222.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
117.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms	(pow (+ 1.0 (/ i n)) n)
105.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

275.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
258.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
209.0ms	(pow (+ 1.0 (/ i n)) n)
364.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify903.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (281.0ms)

Iter	Nodes	Cost
0	244	2124
1	650	2020
2	2077	1796
done	5001	1796

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.2b

localize10.0ms

Local error

Found 3 expressions with local error:

1.9b	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
6.3b	(pow (+ 1.0 (/ i n)) n)
8.7b	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`distribute-rgt-out`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`div-inv`
5×	`add-log-exp`
4×	`pow1` `distribute-lft-neg-out` `unpow-prod-down` `associate-/l*`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3-+` `div-sub` `unsub-neg` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `sum-log` `associate-/r/` `distribute-lft-out` `sqr-pow`

Counts

3 → 120

Calls

3 calls:

14.0ms	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
12.0ms	(pow (+ 1.0 (/ i n)) n)
50.0ms	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

series873.0ms

Counts

3 → 9

Calls

3 calls:

274.0ms	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
212.0ms	(pow (+ 1.0 (/ i n)) n)
386.0ms	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

simplify914.0ms

Counts

129 → 129

Iterations

Useful iterations: done (909.0ms)

Iter	Nodes	Cost
0	273	3420
1	671	2891
2	2295	2740
done	5000	2737

prune362.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.0b	(/ (* (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) n) i)
2.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)

rewrite607.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`add-exp-log` `*-un-lft-identity`
15×	`add-cbrt-cube`
10×	`add-cube-cbrt`
7×	`pow1` `associate-r`
6×	`unpow-prod-down` `add-log-exp` `difference-of-squares`
4×	`associate-*r/` `prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `sub-neg` `pow-unpow` `flip3--` `times-frac` `div-exp` `associate-l` `associate-/r*` `flip--` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

218.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
256.0ms	(/ (* (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) n) i)
114.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms	(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts

4 → 12

Calls

4 calls:

265.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
365.0ms	(/ (* (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) n) i)
249.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms	(pow (+ 1.0 (/ i n)) n)

simplify897.0ms

Counts

99 → 99

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	195	1626
1	491	1548
2	1666	1366
done	5000	1362

prune219.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

regimes123.0ms

Accuracy

55.5% (9.7b remaining)

Error of 21.0b against oracle of 11.3b and baseline of 33.2b

bsearch120.0ms

Steps

Iters	Range		Point
3	9.199102238044756e-11	1.1303867620315504e-10	1.1172319783923582e-10
8	-5195.044129302536	-1.046355961971052	-1.070226988062184

simplify12.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	41	76
1	62	72
2	65	72
3	66	72
done	66	72

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.9s	1034×	body	2560	valid
1.7s	2509×	body	1280	valid
460.0ms	1579×	body	640	valid
146.0ms	902×	body	320	valid
123.0ms	2943×	body	80	valid
71.0ms	2320×	body	80	nan
45.0ms	421×	body	160	valid
24.0ms	6×	body	5120	valid