Details

sample71.0ms

Algorithm

intervals

Results

20.0ms	54×	body	1280	valid
10.0ms	253×	body	80	nan
9.0ms	142×	body	80	valid
8.0ms	35×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize19.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite47.0ms

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:

37.0ms	(- (log (+ N 1.0)) (log N))
6.0ms	(log (+ N 1.0))

series173.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(- (log (+ N 1.0)) (log N))
53.0ms	(log (+ N 1.0))

simplify1.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1090
1	287
0	127

prune339.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.5b	(log (/ (+ N 1.0) N))

rewrite45.0ms

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:

29.0ms	(/ (+ N 1.0) N)
12.0ms	(log (/ (+ N 1.0) N))

series204.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (+ N 1.0) N)
137.0ms	(log (/ (+ N 1.0) N))

simplify890.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1063
1	252
0	112

prune340.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.5b	(log (sqrt (/ (+ N 1.0) N)))
2.5b	(log (sqrt (/ (+ N 1.0) N)))

rewrite43.0ms

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×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

8.0ms	(sqrt (/ (+ N 1.0) N))
8.0ms	(sqrt (/ (+ N 1.0) N))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))
15.0ms	(log (sqrt (/ (+ N 1.0) N)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (/ (+ N 1.0) N))
53.0ms	(sqrt (/ (+ N 1.0) N))
147.0ms	(log (sqrt (/ (+ N 1.0) N)))
134.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify2.9s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
3	1975
2	512
1	211
0	127

prune782.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (/ (+ N 1.0) N)))
2.5b	(log (sqrt (/ (+ N 1.0) N)))
2.7b	(log (sqrt (sqrt (/ (+ N 1.0) N))))
2.7b	(log (sqrt (sqrt (/ (+ N 1.0) N))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

123×	`sqrt-prod`
66×	`*-un-lft-identity`
63×	`log-prod`
49×	`times-frac`
46×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
14×	`pow1`
13×	`sqrt-pow1` `log-pow`
12×	`distribute-lft-out`
7×	`pow1/2` `sqrt-div` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `log-div` `rem-log-exp`

Counts

4 → 145

Calls

4 calls:

10.0ms	(sqrt (sqrt (/ (+ N 1.0) N)))
9.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
8.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

series805.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (sqrt (/ (+ N 1.0) N)))
195.0ms	(log (sqrt (/ (+ N 1.0) N)))
225.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
240.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

simplify2.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
3	3635
2	878
1	359
0	221

prune979.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.6b

bsearch38.0ms

Steps

Iters	Range		Point
7	160.65039477392645	5787.9300826946865	5705.4022801559

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample3.0s

Algorithm

intervals

Results

869.0ms	1783×	body	1280	valid
810.0ms	1303×	body	640	valid
417.0ms	7946×	body	80	nan
325.0ms	4055×	body	80	valid
98.0ms	557×	body	320	valid
33.0ms	302×	body	160	valid