Details

sample266.0ms

Algorithm

intervals

Results

104.0ms	34×	body	2560	valid
87.0ms	77×	body	1280	valid
27.0ms	48×	body	640	valid
13.0ms	113×	body	80	valid
8.0ms	24×	body	320	valid
7.0ms	70×	body	80	nan
3.0ms	11×	body	160	valid

simplify958.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
5	2016
4	533
3	154
2	59
1	28
0	10

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
7.1b	(pow (+ 1 (/ i n)) n)
9.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite547.0ms

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:

181.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
134.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
211.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

429.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
304.0ms	(- (pow (+ 1 (/ i n)) n) 1)
306.0ms	(pow (+ 1 (/ i n)) n)
376.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.6s

Counts

508 → 508

Iterations

Iter	Nodes
done	2000
2	2000
1	1844
0	583

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
0.1b	(* (log (+ 1 (/ i n))) n)
9.8b	(log (+ 1 (/ i n)))
9.9b	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
96×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
85×	`add-cube-cbrt`
47×	`associate-r`
21×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`pow1`
9×	`div-inv`
7×	`associate-l`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log-prod` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`log-div` `pow-prod-down` `associate-/r/` `log-pow` `*-commutative`
1×	`clear-num` `frac-2neg` `log1p-def` `flip3-+` `div-sub` `rem-log-exp` `associate-*r/` `flip-+` `distribute-lft-out` `expm1-udef`

Counts

4 → 184

Calls

4 calls:

12.0ms	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
7.0ms	(* (log (+ 1 (/ i n))) n)
4.0ms	(log (+ 1 (/ i n)))
6.0ms	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

424.0ms	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
126.0ms	(* (log (+ 1 (/ i n))) n)
89.0ms	(log (+ 1 (/ i n)))
427.0ms	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

simplify1.1s

Counts

196 → 196

Iterations

Iter	Nodes
done	2001
2	2001
1	782
0	297

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
7.0b	(log1p (/ i n))
9.8b	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))
9.9b	(* (log1p (/ i n)) n)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
84×	`*-un-lft-identity` `add-cube-cbrt`
47×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
9×	`div-inv`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-l`
5×	`expm1-log1p-u`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`pow-prod-down` `associate-/r/` `*-commutative`
1×	`log1p-udef` `clear-num` `frac-2neg` `div-sub` `log1p-expm1` `associate-*r/` `expm1-udef`

Counts

4 → 176

Calls

4 calls:

12.0ms	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
0.0ms	(log1p (/ i n))
10.0ms	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))
6.0ms	(* (log1p (/ i n)) n)

series739.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
59.0ms	(log1p (/ i n))
293.0ms	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))
81.0ms	(* (log1p (/ i n)) n)

simplify660.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	2001
2	2001
1	730
0	276

prune627.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (expm1 (* (log1p (/ i n)) n)))
7.0b	(log1p (/ i n))
9.9b	(* (log1p (/ i n)) n)
9.9b	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
26×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow-prod-down` `*-commutative` `unswap-sqr`
1×	`log1p-udef` `clear-num` `frac-2neg` `log1p-expm1` `associate-/r/` `associate-/l*`

Counts

4 → 103

Calls

4 calls:

5.0ms	(* 100 (expm1 (* (log1p (/ i n)) n)))
0.0ms	(log1p (/ i n))
6.0ms	(* (log1p (/ i n)) n)
10.0ms	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

series674.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* 100 (expm1 (* (log1p (/ i n)) n)))
58.0ms	(log1p (/ i n))
75.0ms	(* (log1p (/ i n)) n)
306.0ms	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

simplify872.0ms

Counts

115 → 115

Iterations

Iter	Nodes
done	2004
3	2004
2	1652
1	487
0	201

prune344.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.4b

regimes202.0ms

Accuracy

16.6% (8.9b remaining)

Error of 18.5b against oracle of 9.6b and baseline of 20.3b

bsearch482.0ms

Steps

Iters	Range		Point
8	2.777301318491332e-263	7.2525602558216025e-261	7.188766975051312e-261
9	-4.2446029499057394e-109	-1.499370768437365e-117	-1.2129113627355937e-111
9	-1.6931687773033811e-68	-1.0581846654483799e-75	-5.215706912201119e-75
11	-1.2475612113013005e+20	-0.005838610583870787	-1.2657089139394981

simplify10.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.2s	2493×	body	1280	valid
2.7s	973×	body	2560	valid
1.0s	1635×	body	640	valid
732.0ms	3042×	body	80	valid
377.0ms	831×	body	320	valid
265.0ms	2287×	body	80	nan
124.0ms	477×	body	160	valid
49.0ms	10×	body	5120	valid