Details

sample407.0ms

Algorithm

intervals

Results

166.0ms	41×	body	2560	valid
142.0ms	77×	body	1280	valid
32.0ms	37×	body	640	valid
16.0ms	28×	body	320	valid
13.0ms	85×	body	80	valid
11.0ms	77×	body	80	nan
7.0ms	19×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	7344
5	1457
4	432
3	152
2	57
1	26
0	10

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 47.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.6b	(- (pow (+ 1 (/ i n)) n) 1)
9.2b	(pow (+ 1 (/ i n)) n)
12.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite651.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
501×	`add-sqr-sqrt`
390×	`*-un-lft-identity`
240×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
104×	`unpow-prod-down`
89×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
24×	`prod-diff`
21×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
8×	`fma-neg`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 496

Calls

4 calls:

265.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
145.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
218.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

395.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
320.0ms	(- (pow (+ 1 (/ i n)) n) 1)
308.0ms	(pow (+ 1 (/ i n)) n)
451.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify6.5s

Counts

508 → 508

Iterations

Iter	Nodes
2	5114
1	1746
0	583

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.9b

localize23.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* n (log1p (/ i n)))) 1)
7.1b	(log1p (/ i n))
12.6b	(* n (log1p (/ i n)))
13.0b	(/ (- (exp (* n (log1p (/ i n)))) 1) (/ i n))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
145×	`add-sqr-sqrt`
128×	`*-un-lft-identity`
83×	`add-cube-cbrt`
30×	`difference-of-squares`
15×	`difference-of-sqr-1` `distribute-lft-out--`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff` `div-inv`
7×	`associate-/l*`
6×	`pow1` `add-log-exp`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`expm1-def` `log1p-udef` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 197

Calls

4 calls:

14.0ms	(- (exp (* n (log1p (/ i n)))) 1)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))
28.0ms	(/ (- (exp (* n (log1p (/ i n)))) 1) (/ i n))

series721.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(- (exp (* n (log1p (/ i n)))) 1)
59.0ms	(log1p (/ i n))
66.0ms	(* n (log1p (/ i n)))
351.0ms	(/ (- (exp (* n (log1p (/ i n)))) 1) (/ i n))

simplify2.5s

Counts

209 → 209

Iterations

Iter	Nodes
2	3096
1	958
0	349

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* n (expm1 i))
0.1b	(* 100 (/ (* n (expm1 i)) i))
5.9b	(/ (* n (expm1 i)) i)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
10×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`pow1`
6×	`times-frac` `associate-l` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-r/` `associate-/l`

Counts

3 → 75

Calls

3 calls:

6.0ms	(* n (expm1 i))
13.0ms	(* 100 (/ (* n (expm1 i)) i))
9.0ms	(/ (* n (expm1 i)) i)

series154.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* n (expm1 i))
58.0ms	(* 100 (/ (* n (expm1 i)) i))
52.0ms	(/ (* n (expm1 i)) i)

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
3	5194
2	1093
1	323
0	134

prune503.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (expm1 i) i)
0.8b	(* (* 100 n) (/ (expm1 i) i))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `associate-/r` `div-exp` `pow-prod-down` `associate-/l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `div-sub` `associate-l` `associate-r/` `-commutative` `expm1-udef`

Counts

2 → 67

Calls

2 calls:

7.0ms	(/ (expm1 i) i)
27.0ms	(* (* 100 n) (/ (expm1 i) i))

series133.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (expm1 i) i)
76.0ms	(* (* 100 n) (/ (expm1 i) i))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
3	4633
2	1175
1	337
0	127

prune418.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes164.0ms

Accuracy

51.6% (10.5b remaining)

Error of 10.6b against oracle of 0.1b and baseline of 21.8b

bsearch591.0ms

Steps

Iters	Range		Point
9	0.00043643909784968257	1213.337773267216	228.0818158074512
8	7.262047858377854e-186	4.422991971728374e-183	7.328121567592983e-186
9	-1.5668037355847878e-226	-2.9695246138863732e-235	-7.207093076091718e-232
11	-774963815.1405225	-6.948120050383171e-19	-5.946757000840379

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	30

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.3s	2499×	body	1280	valid
2.7s	990×	body	2560	valid
1.0s	1595×	body	640	valid
376.0ms	3022×	body	80	valid
321.0ms	825×	body	320	valid
299.0ms	2323×	body	80	nan
124.0ms	425×	body	160	valid
34.0ms	7×	body	5120	valid