Details

sample431.0ms

Algorithm

intervals

Results

105.0ms	256×	body	80	nan
102.0ms	122×	body	80	valid
51.0ms	53×	body	640	valid
42.0ms	47×	body	1280	valid
15.0ms	24×	body	320	valid
6.0ms	10×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize47.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
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:

37.0ms	(- (log (+ N 1.0)) (log N))
14.0ms	(log (+ N 1.0))

series821.0ms

Counts

2 → 6

Calls

2 calls:

454.0ms	(- (log (+ N 1.0)) (log N))
351.0ms	(log (+ N 1.0))

simplify12.5s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	4900
3	1602
2	528
1	213
0	101

prune830.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.5b	(/ 0.5 (* N N))
11.8b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite529.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

63.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
65.0ms	(/ (/ 0.3333333333333333 N) (* N N))
17.0ms	(/ 0.5 (* N N))
377.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
195.0ms	(/ (/ 0.3333333333333333 N) (* N N))
53.0ms	(/ 0.5 (* N N))
69.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

simplify6.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1862
1	538
0	210

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite67.0ms

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×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
15.0ms	(log (/ (+ N 1.0) N))

series621.0ms

Counts

2 → 6

Calls

2 calls:

352.0ms	(/ (+ N 1.0) N)
268.0ms	(log (/ (+ N 1.0) N))

simplify7.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2332
2	617
1	243
0	108

prune708.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (log (+ N 1.0)) (log N))
3.2b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))
3.6b	(log (+ N 1.0))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
22×	`log-prod`
14×	`pow1` `add-sqr-sqrt`
10×	`add-cube-cbrt` `log-pow`
8×	`log-div` `associate--l+` `distribute-lft-out--`
6×	`add-exp-log` `associate--r+`
4×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

87.0ms	(- (log (+ N 1.0)) (log N))
240.0ms	(- (log (+ N 1.0)) (log N))
9.0ms	(log (+ N 1.0))
9.0ms	(log (+ N 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

612.0ms	(- (log (+ N 1.0)) (log N))
584.0ms	(- (log (+ N 1.0)) (log N))
113.0ms	(log (+ N 1.0))
205.0ms	(log (+ N 1.0))

simplify14.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
4	4900
3	1602
2	528
1	213
0	101

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch2.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample11.3s

Algorithm

intervals

Results

3.8s	1720×	body	1280	valid
2.7s	314×	body	160	valid
2.0s	7895×	body	80	nan
1.4s	4129×	body	80	valid
614.0ms	1230×	body	640	valid
195.0ms	607×	body	320	valid