Details

sample297.0ms

Algorithm

intervals

Results

120.0ms	83×	body	1280	valid
63.0ms	18×	body	2560	valid
31.0ms	42×	body	640	valid
22.0ms	74×	body	80	nan
19.0ms	36×	body	320	valid
16.0ms	113×	body	80	valid
6.0ms	19×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	6722
5	1463
4	420
3	150
2	58
1	28
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.0b	(- (pow (+ 1 (/ i n)) n) 1)
5.1b	(pow (+ 1 (/ i n)) n)
8.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`insert-posit16`
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 → 453

Calls

4 calls:

208.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
97.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)
217.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

453.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
279.0ms	(- (pow (+ 1 (/ i n)) n) 1)
282.0ms	(pow (+ 1 (/ i n)) n)
379.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify2.5s

Counts

465 → 465

Iterations

Iter	Nodes
2	5084
1	1658
0	542

prune5.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.9b

localize56.0ms

Local error

Found 4 expressions with local error:

5.1b	(pow (+ (/ i n) 1) n)
5.1b	(pow (+ (/ i n) 1) n)
5.1b	(pow (+ (/ i n) 1) n)
8.2b	(/ (/ (- (* (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)) (pow (+ (/ i n) 1) n)) 1) (+ (+ (pow (+ (/ i n) 1) n) 1) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)))) (/ i n))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

465×	`times-frac`
226×	`*-un-lft-identity`
220×	`add-sqr-sqrt` `add-cube-cbrt`
31×	`div-inv`
29×	`associate-/r/`
19×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`associate-/l*`
14×	`flip3-+` `flip-+`
13×	`associate-/r*`
12×	`unpow-prod-down`
9×	`pow-unpow`
8×	`cbrt-undiv` `div-exp`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`
2×	`div-sub`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 302

Calls

4 calls:

24.0ms	(pow (+ (/ i n) 1) n)
24.0ms	(pow (+ (/ i n) 1) n)
25.0ms	(pow (+ (/ i n) 1) n)
963.0ms	(/ (/ (- (* (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)) (pow (+ (/ i n) 1) n)) 1) (+ (+ (pow (+ (/ i n) 1) n) 1) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)))) (/ i n))

series7.9s

Counts

4 → 12

Calls

4 calls:

305.0ms	(pow (+ (/ i n) 1) n)
249.0ms	(pow (+ (/ i n) 1) n)
270.0ms	(pow (+ (/ i n) 1) n)
7.1s	(/ (/ (- (* (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)) (pow (+ (/ i n) 1) n)) 1) (+ (+ (pow (+ (/ i n) 1) n) 1) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)))) (/ i n))

simplify4.0s

Counts

314 → 314

Iterations

Iter	Nodes
2	7079
1	1821
0	560

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.2b	(/ 1 (/ i n))
5.1b	(pow (+ 1 (/ i n)) n)
9.9b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

395×	`times-frac`
286×	`add-sqr-sqrt`
233×	`*-un-lft-identity`
153×	`add-cube-cbrt`
70×	`unpow-prod-down`
35×	`difference-of-squares`
29×	`add-exp-log`
26×	`associate-/r*`
25×	`sqr-pow`
24×	`div-inv`
16×	`div-exp` `distribute-lft-out--`
15×	`distribute-lft-out`
14×	`add-cbrt-cube`
11×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `add-log-exp`
5×	`distribute-rgt-out--` `associate-/r/`
4×	`insert-posit16`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `pow-pow` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 312

Calls

4 calls:

27.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
6.0ms	(/ 1 (/ i n))
8.0ms	(pow (+ 1 (/ i n)) n)
110.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
10.0ms	(/ 1 (/ i n))
285.0ms	(pow (+ 1 (/ i n)) n)
376.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify1.1s

Counts

324 → 324

Iterations

Iter	Nodes
2	3214
1	1200
0	487

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
0.2b	(* 1/6 (* n (* i i)))
5.9b	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
6.4b	(* n (* i i))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in`

Counts

4 → 79

Calls

4 calls:

45.0ms	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
34.0ms	(* 1/6 (* n (* i i)))
36.0ms	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
14.0ms	(* n (* i i))

series227.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* 100 (+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2))))
33.0ms	(* 1/6 (* n (* i i)))
70.0ms	(+ (+ n (* 1/6 (* n (* i i)))) (* i (* n 1/2)))
28.0ms	(* n (* i i))

simplify3.9s

Counts

91 → 91

Iterations

Iter	Nodes
3	9098
2	1508
1	376
0	132

prune697.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.3b

regimes333.0ms

Accuracy

39.2% (16.8b remaining)

Error of 22.8b against oracle of 5.9b and baseline of 33.6b

bsearch770.0ms

Steps

Iters	Range		Point
7	1.5907932585176938e-94	4.4505383751806786e-93	1.658674653647369e-94
6	-6150560963.103066	-878088654.311629	-889817905.8903499
8	-4.2581589608976594e+99	-9.564291913640547e+94	-2.5419696905962584e+96
6	-3.0677740643837958e+231	-3.849879583071603e+230	-6.812585307839581e+230

simplify13.0ms

Iterations

Iter	Nodes
2	49
1	49
0	36

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.0s	2460×	body	1280	valid
2.6s	973×	body	2560	valid
998.0ms	1594×	body	640	valid
657.0ms	3089×	body	80	valid
410.0ms	879×	body	320	valid
229.0ms	2233×	body	80	nan
111.0ms	448×	body	160	valid
42.0ms	8×	body	5120	valid