Details

sample84.0ms

Algorithm

intervals

Results

22.0ms	50×	body	1280	valid
15.0ms	312×	body	80	nan
13.0ms	48×	body	640	valid
9.0ms	123×	body	80	valid
5.0ms	28×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize35.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1.0)) (log N))
3.0b	(log (+ N 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

22.0ms	(- (log (+ N 1.0)) (log N))
8.0ms	(log (+ N 1.0))

series511.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(- (log (+ N 1.0)) (log N))
396.0ms	(log (+ N 1.0))

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1090
1	287
0	127

prune271.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
0.1b	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
0.1b	(/ (/ 1 N) N)

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

201×	`times-frac`
167×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
149×	`add-cube-cbrt`
78×	`prod-diff`
43×	`associate-l`
41×	`distribute-rgt-in` `distribute-lft-in`
27×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`div-inv`
13×	`associate-/l*`
12×	`div-exp`
8×	`pow1`
6×	`cbrt-undiv` `associate-r`
5×	`prod-exp` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rec-exp` `sub-neg` `flip3--` `1-exp` `associate-*r/` `flip--` `difference-of-squares` `pow-div`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `pow-flip` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

3 → 246

Calls

3 calls:

0.0ms	(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
102.0ms	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
21.0ms	(/ (/ 1 N) N)

series226.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
125.0ms	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
33.0ms	(/ (/ 1 N) N)

simplify1.2s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
1	1227
0	416

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

2.4b	(log (/ (+ N 1.0) N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `div-exp` `log-pow` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

9.0ms

(log (/ (+ N 1.0) N))

series118.0ms

Counts

1 → 3

Calls

1 calls:

118.0ms

(log (/ (+ N 1.0) N))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
3	1934
2	467
1	173
0	86

prune175.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
2.5b	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
48×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`log-prod`
33×	`sqrt-prod`
28×	`associate-+r+`
19×	`distribute-lft-out`
16×	`fma-def`
14×	`pow1` `log-pow`
10×	`distribute-rgt-neg-in`
6×	`distribute-lft-neg-in` `associate-+l+` `distribute-neg-in` `associate-/r*` `add-exp-log`
5×	`add-cbrt-cube`
4×	`associate-/l*` `add-log-exp`
3×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u`
2×	`sum-log` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `log-div` `clear-num` `associate-+r-` `neg-mul-1` `frac-2neg` `div-exp` `rem-log-exp` `neg-log` `associate-+l-`

Counts

3 → 141

Calls

3 calls:

2.0ms	(log (sqrt N))
15.0ms	(/ (+ N 1.0) (sqrt N))
45.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series373.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(log (sqrt N))
64.0ms	(/ (+ N 1.0) (sqrt N))
239.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1976
1	486
0	205

prune670.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.9b

bsearch32.0ms

Steps

Iters	Range		Point
9	4.9803363081918155	573579.0075499975	8915.293301236256

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

696.0ms	1676×	body	1280	valid
486.0ms	7998×	body	80	nan
354.0ms	1264×	body	640	valid
323.0ms	4128×	body	80	valid
144.0ms	665×	body	320	valid
28.0ms	267×	body	160	valid