Details

sample77.0ms

Algorithm

intervals

Results

21.0ms	50×	body	1280	valid
13.0ms	312×	body	80	nan
12.0ms	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

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

10.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series219.0ms

Counts

2 → 6

Calls

2 calls:

142.0ms	(- (log (+ N 1.0)) (log N))
77.0ms	(log (+ N 1.0))

simplify1.5s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	2789
2	645
1	213
0	101

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.4b	(/ 0.5 (* N N))
16.1b	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
39×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp` `difference-of-squares`
6×	`frac-sub` `div-inv`
5×	`distribute-lft-out--`
4×	`pow1` `diff-log`
3×	`sub-neg` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate--r+` `sub-div`
1×	`distribute-rgt-out--` `associate--r-` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

93.0ms	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
12.0ms	(/ (/ 0.3333333333333333 N) (* N N))
12.0ms	(/ 0.5 (* N N))
54.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
55.0ms	(/ (/ 0.3333333333333333 N) (* N N))
43.0ms	(/ 0.5 (* N N))
134.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

simplify2.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	3082
1	602
0	223

prune590.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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×	`log-div` `add-cbrt-cube` `div-exp` `log-pow` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

5.0ms

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

series136.0ms

Counts

1 → 3

Calls

1 calls:

135.0ms

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

simplify1.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
3	1859
2	452
1	169
0	84

prune137.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
48×	`times-frac`
40×	`log-prod`
39×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`sqrt-prod`
28×	`associate-+r+`
19×	`distribute-lft-out`
10×	`pow1`
8×	`log-pow`
6×	`associate-+l+` `distribute-neg-in` `associate-/r*` `add-exp-log`
5×	`add-cbrt-cube`
4×	`distribute-rgt-neg-in` `associate-/l*` `add-log-exp`
2×	`sum-log` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `log-div` `clear-num` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `neg-log` `associate-+l-`

Counts

3 → 119

Calls

3 calls:

3.0ms	(log (sqrt N))
30.0ms	(/ (+ 1.0 N) (sqrt N))
26.0ms	(+ (- (log (sqrt N))) (log (/ (+ 1.0 N) (sqrt N))))

series425.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(log (sqrt N))
78.0ms	(/ (+ 1.0 N) (sqrt N))
266.0ms	(+ (- (log (sqrt N))) (log (/ (+ 1.0 N) (sqrt N))))

simplify1.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1894
1	464
0	199

prune549.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch64.0ms

Steps

Iters	Range		Point
9	4.9803363081918155	573579.0075499975	8915.293301236256

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

839.0ms	1264×	body	640	valid
783.0ms	1676×	body	1280	valid
540.0ms	7998×	body	80	nan
370.0ms	4128×	body	80	valid
135.0ms	665×	body	320	valid
79.0ms	267×	body	160	valid