Details

sample56.0ms

Algorithm

intervals

Results

16.0ms	56×	body	1280	valid
9.0ms	288×	body	80	nan
8.0ms	142×	body	80	valid
6.0ms	31×	body	640	valid
3.0ms	21×	body	320	valid
0.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize10.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ 1.0 N)) (log N))
3.2b	(log (+ 1.0 N))

rewrite18.0ms

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:

12.0ms	(- (log (+ 1.0 N)) (log N))
4.0ms	(log (+ 1.0 N))

series235.0ms

Counts

2 → 6

Calls

2 calls:

169.0ms	(- (log (+ 1.0 N)) (log N))
66.0ms	(log (+ 1.0 N))

simplify1.0s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1091
1	287
0	126

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.3b	(log (/ (+ N 1.0) N))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

17.0ms	(/ (+ N 1.0) N)
5.0ms	(log (/ (+ N 1.0) N))

series195.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(/ (+ N 1.0) N)
117.0ms	(log (/ (+ N 1.0) N))

simplify642.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1063
1	252
0	112

prune277.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

196×	`prod-diff`
140×	`unpow-prod-down` `cube-prod`
118×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
81×	`pow1`
77×	`log-pow`
37×	`sqr-pow`
29×	`cube-mult` `unpow3`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 309

Calls

4 calls:

50.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
4.0ms	(log (+ N 1.0))
4.0ms	(log (+ N 1.0))
9.0ms	(log (+ N 1.0))

series436.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
46.0ms	(log (+ N 1.0))
60.0ms	(log (+ N 1.0))
48.0ms	(log (+ N 1.0))

simplify2.6s

Counts

321 → 321

Iterations

Iter	Nodes
done	5000
2	3783
1	827
0	323

prune733.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
0.1b	(/ (/ 1 N) N)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 236

Calls

2 calls:

103.0ms	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
9.0ms	(/ (/ 1 N) N)

series145.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
20.0ms	(/ (/ 1 N) N)

simplify775.0ms

Counts

242 → 242

Iterations

Iter	Nodes
done	5001
1	1195
0	399

prune623.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch38.0ms

Steps

Iters	Range		Point
8	5.1212688054922095	43837.056983701754	7426.10510392418

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample2.7s

Algorithm

intervals

Results

731.0ms	1688×	body	1280	valid
535.0ms	7906×	body	80	nan
411.0ms	4067×	body	80	valid
404.0ms	1295×	body	640	valid
122.0ms	668×	body	320	valid
37.0ms	282×	body	160	valid