Details

sample104.0ms

Algorithm

intervals

Results

31.0ms	312×	body	80	nan
23.0ms	50×	body	1280	valid
16.0ms	48×	body	640	valid
10.0ms	123×	body	80	valid
6.0ms	28×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

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

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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:

15.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series222.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(- (log (+ N 1.0)) (log N))
83.0ms	(log (+ N 1.0))

simplify3.0s

Counts

47 → 47

Iterations

Iter	Nodes
done	5003
4	4941
3	1603
2	538
1	213
0	101

prune258.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N))) (/ 1.0 N))
0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.4b	(/ 0.5 (* N N))
12.8b	(- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
34×	`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`
6×	`div-inv` `difference-of-squares`
4×	`pow1` `frac-add`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out` `sub-div`
1×	`+-commutative` `flip3-+` `distribute-rgt-out--` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 111

Calls

4 calls:

198.0ms	(+ (- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N))) (/ 1.0 N))
11.0ms	(/ (/ 0.3333333333333333 N) (* N N))
6.0ms	(/ 0.5 (* N N))
61.0ms	(- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N))) (/ 1.0 N))
50.0ms	(/ (/ 0.3333333333333333 N) (* N N))
40.0ms	(/ 0.5 (* N N))
120.0ms	(- (/ (/ 0.3333333333333333 N) (* N N)) (/ 0.5 (* N N)))

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	1816
1	553
0	215

prune561.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

series111.0ms

Counts

1 → 3

Calls

1 calls:

111.0ms

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

simplify2.3s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
4	3461
3	1027
2	349
1	169
0	84

prune119.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

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))))

rewrite48.0ms

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:

2.0ms	(log (sqrt N))
16.0ms	(/ (+ N 1.0) (sqrt N))
25.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series417.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(log (sqrt N))
65.0ms	(/ (+ N 1.0) (sqrt N))
278.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1294
1	463
0	199

prune525.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

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

bsearch48.0ms

Steps

Iters	Range		Point
9	4.9803363081918155	573579.0075499975	8915.293301236256

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

784.0ms	1676×	body	1280	valid
688.0ms	665×	body	320	valid
361.0ms	7998×	body	80	nan
340.0ms	1264×	body	640	valid
321.0ms	4128×	body	80	valid
31.0ms	267×	body	160	valid