Details

sample81.0ms

Algorithm

intervals

Results

24.0ms	51×	body	1280	valid
16.0ms	303×	body	80	nan
12.0ms	37×	body	640	valid
11.0ms	135×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	15×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize13.0ms

Local error

Found 2 expressions with local error:

4.2b	(log (+ N 1))
4.6b	(- (log (+ N 1)) (log N))

rewrite33.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

17.0ms	(log (+ N 1))
15.0ms	(- (log (+ N 1)) (log N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(log (+ N 1))
94.0ms	(- (log (+ N 1)) (log N))

simplify2.6s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	3864
3	1350
2	463
1	199
0	97

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
4.8b	(log (/ (+ N 1) N))

rewrite24.0ms

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` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

16.0ms	(/ (+ N 1) N)
7.0ms	(log (/ (+ N 1) N))

series145.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(/ (+ N 1) N)
71.0ms	(log (/ (+ N 1) N))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5021
3	2563
2	620
1	233
0	102

prune217.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1) N))
0.1b	(sqrt (/ (+ N 1) N))
4.8b	(log (sqrt (/ (+ N 1) N)))
4.8b	(log (sqrt (/ (+ N 1) N)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`log-prod` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 122

Calls

4 calls:

10.0ms	(sqrt (/ (+ N 1) N))
11.0ms	(sqrt (/ (+ N 1) N))
8.0ms	(log (sqrt (/ (+ N 1) N)))
9.0ms	(log (sqrt (/ (+ N 1) N)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (/ (+ N 1) N))
49.0ms	(sqrt (/ (+ N 1) N))
72.0ms	(log (sqrt (/ (+ N 1) N)))
99.0ms	(log (sqrt (/ (+ N 1) N)))

simplify2.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
4	3056
3	1011
2	415
1	202
0	124

prune590.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ N 1) N)
0.1b	(sqrt (/ (+ N 1) N))
4.8b	(log (/ (+ N 1) N))
4.8b	(log (sqrt (/ (+ N 1) N)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
49×	`times-frac`
41×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
35×	`log-prod`
32×	`sqrt-prod`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
4×	`log-pow` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `rem-log-exp`
2×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+`

Counts

4 → 123

Calls

4 calls:

27.0ms	(/ (+ N 1) N)
11.0ms	(sqrt (/ (+ N 1) N))
7.0ms	(log (/ (+ N 1) N))
8.0ms	(log (sqrt (/ (+ N 1) N)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (+ N 1) N)
42.0ms	(sqrt (/ (+ N 1) N))
82.0ms	(log (/ (+ N 1) N))
90.0ms	(log (sqrt (/ (+ N 1) N)))

simplify2.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
3	3273
2	900
1	363
0	186

prune666.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch45.0ms

Steps

Iters	Range		Point
8	9038.04311539703	45027090.2690009	9233.861277203294

simplify7.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

844.0ms	1684×	body	1280	valid
701.0ms	4127×	body	80	valid
517.0ms	8149×	body	80	nan
439.0ms	1266×	body	640	valid
120.0ms	626×	body	320	valid
35.0ms	297×	body	160	valid