Details

sample350.0ms

Algorithm

intervals

Results

138.0ms	79×	body	1280	valid
124.0ms	38×	body	2560	valid
37.0ms	50×	body	640	valid
11.0ms	27×	body	320	valid
11.0ms	89×	body	80	valid
9.0ms	77×	body	80	nan
3.0ms	12×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2473
4	512
3	150
2	58
1	28
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
2.7b	(- (pow (+ 1 (/ i n)) n) 1)
5.2b	(pow (+ 1 (/ i n)) n)
12.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

593×	`times-frac`
506×	`add-sqr-sqrt`
386×	`*-un-lft-identity`
236×	`add-cube-cbrt`
182×	`associate-r`
174×	`difference-of-squares`
91×	`unpow-prod-down`
88×	`sqr-pow`
87×	`difference-of-sqr-1`
34×	`associate-/l*`
32×	`associate-/r*`
31×	`associate-*r/`
30×	`div-inv` `distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube` `associate-/r/`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`clear-num`
4×	`frac-2neg` `insert-posit16` `associate-/l/`
3×	`pow-unpow` `flip3--` `associate-l` `prod-exp` `un-div-inv` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `*-commutative` `distribute-lft-out`

Counts

4 → 502

Calls

4 calls:

792.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
212.0ms	(- (pow (+ 1 (/ i n)) n) 1)
17.0ms	(pow (+ 1 (/ i n)) n)
385.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

421.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
294.0ms	(- (pow (+ 1 (/ i n)) n) 1)
261.0ms	(pow (+ 1 (/ i n)) n)
416.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify2.2s

Counts

514 → 514

Iterations

Iter	Nodes
done	5002
1	1865
0	579

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* i i) i)
0.1b	(* 1/6 (* (* i i) i))
4.5b	(+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i))
18.2b	(/ (+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i)) (/ i n))

rewrite4.3s

Algorithm

rewrite-expression-head

Rules

691×	`*-un-lft-identity`
449×	`times-frac`
285×	`distribute-lft-out`
250×	`associate-r`
249×	`associate-l`
222×	`add-sqr-sqrt`
181×	`add-cube-cbrt`
120×	`distribute-rgt-out`
69×	`*-commutative`
60×	`distribute-rgt1-in`
32×	`pow1`
26×	`unswap-sqr`
23×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
22×	`div-inv`
16×	`associate-/r*`
9×	`swap-sqr` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
6×	`pow-plus` `pow-prod-up`
4×	`insert-posit16`
3×	`cbrt-undiv` `sum-log` `div-exp`
2×	`pow2` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `flip3-+` `pow3` `pow-sqr` `flip-+` `associate-/l/`

Counts

4 → 454

Calls

4 calls:

31.0ms	(* (* i i) i)
127.0ms	(* 1/6 (* (* i i) i))
1.2s	(+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i))
2.9s	(/ (+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i)) (/ i n))

series231.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* i i) i)
47.0ms	(* 1/6 (* (* i i) i))
40.0ms	(+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i))
93.0ms	(/ (+ (+ i (* 1/6 (* (* i i) i))) (* (* 1/2 i) i)) (/ i n))

simplify2.6s

Counts

466 → 466

Iterations

Iter	Nodes
done	5009
2	3323
1	1065
0	386

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (* i i) i))
1.2b	(* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n)
4.5b	(+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i))
9.6b	(* (/ 1 i) (* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n))

rewrite16.7s

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
124×	`associate-l`
118×	`associate-r`
89×	`add-sqr-sqrt`
60×	`distribute-lft-out`
37×	`add-exp-log`
31×	`associate-*l/`
30×	`add-cube-cbrt` `unswap-sqr`
27×	`distribute-rgt-out` `add-cbrt-cube`
20×	`pow1`
19×	`prod-exp`
18×	`frac-times`
14×	`*-commutative`
13×	`times-frac` `cbrt-unprod`
12×	`flip3-+` `distribute-rgt1-in` `flip-+`
10×	`pow-prod-down`
9×	`associate-/r` `associate-/l` `add-log-exp`
5×	`swap-sqr`
4×	`div-exp` `insert-posit16`
3×	`clear-num` `sum-log` `frac-2neg`
2×	`cbrt-undiv` `+-commutative` `rec-exp` `associate-+l+` `1-exp` `associate-*r/`
1×	`div-inv`

Counts

4 → 228

Calls

4 calls:

126.0ms	(* 1/6 (* (* i i) i))
3.0s	(* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n)
1.2s	(+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i))
12.4s	(* (/ 1 i) (* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n))

series240.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 1/6 (* (* i i) i))
59.0ms	(* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n)
35.0ms	(+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i))
97.0ms	(* (/ 1 i) (* (+ (+ i (* 1/6 (* (* i i) i))) (* (* i 1/2) i)) n))

simplify2.3s

Counts

240 → 240

Iterations

Iter	Nodes
done	5000
2	3753
1	1004
0	301

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n))))
0.2b	(* 1/6 (* i i))
2.6b	(* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)
9.6b	(* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)))

rewrite42.1s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
174×	`associate-r`
107×	`*-un-lft-identity`
103×	`add-exp-log`
83×	`associate-l`
80×	`unswap-sqr`
73×	`associate-*r/`
65×	`prod-exp`
61×	`add-cbrt-cube`
60×	`associate-*l/`
50×	`add-cube-cbrt`
36×	`frac-times` `times-frac`
35×	`cbrt-unprod`
34×	`pow1`
30×	`distribute-lft-out`
21×	`flip3-+` `flip-+`
20×	`pow-prod-down`
18×	`associate-/r` `associate-/l`
12×	`div-exp`
11×	`*-commutative`
6×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
4×	`swap-sqr` `insert-posit16` `add-log-exp`
2×	`div-inv`

Counts

4 → 304

Calls

4 calls:

31.8s	(* 100 (* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n))))
27.0ms	(* 1/6 (* i i))
736.0ms	(* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)
9.6s	(* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 100 (* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n))))
28.0ms	(* 1/6 (* i i))
43.0ms	(* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)
38.0ms	(* (/ 1 i) (* i (* (+ (+ 1 (* 1/6 (* i i))) (* 1/2 i)) n)))

simplify1.3s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1380
0	399

prune892.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.2b

regimes301.0ms

Accuracy

53.2% (10.2b remaining)

Error of 20.1b against oracle of 10.0b and baseline of 31.7b

bsearch952.0ms

Steps

Iters	Range		Point
7	4.048842843541669e+202	5.561071419116658e+204	7.218954252890614e+203
9	3.357902288332178e-05	2.2608459371195293	0.13449167275451146
8	1.7901381506861888e-191	5.790205777606572e-187	3.2268987471607203e-189
8	1.1635774388254012e-232	1.1915484969107771e-228	1.1743359908539163e-228
9	-1.5970922184414271e-257	-7.912477626562658e-263	-1.4365268904089577e-258
5	-4.981612762678325e-05	-1.3178926426525978e-05	-4.890775921786639e-05

simplify42.0ms

Iterations

Iter	Nodes
done	99
1	99
0	69

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.5s	2516×	body	1280	valid
2.4s	1021×	body	2560	valid
960.0ms	1583×	body	640	valid
591.0ms	877×	body	320	valid
417.0ms	386×	body	160	valid
288.0ms	2991×	body	80	valid
221.0ms	2267×	body	80	nan
22.0ms	5×	body	5120	valid