Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	54×	body	1280	valid
12.0ms	253×	body	80	nan
11.0ms	142×	body	80	valid
10.0ms	35×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	222
1	9	222
2	10	222
done	10	222

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize37.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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:

18.0ms	(- (log (+ N 1.0)) (log N))
7.0ms	(log (+ N 1.0))

series257.0ms

Counts

2 → 6

Calls

2 calls:

178.0ms	(- (log (+ N 1.0)) (log N))
79.0ms	(log (+ N 1.0))

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	15630
1	213	12900
2	645	12195
3	2789	12195
done	5000	12044

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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

Counts

2 → 60

Calls

2 calls:

28.0ms	(/ (+ N 1.0) N)
10.0ms	(log (/ (+ N 1.0) N))

series210.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (+ N 1.0) N)
141.0ms	(log (/ (+ N 1.0) N))

simplify844.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	108	17921
1	243	15986
2	1007	15504
done	5000	15504

prune252.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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)))

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` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

8.0ms	(sqrt (/ (+ N 1.0) N))
9.0ms	(sqrt (/ (+ N 1.0) N))
10.0ms	(log (sqrt (/ (+ N 1.0) N)))
11.0ms	(log (sqrt (/ (+ N 1.0) N)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (/ (+ N 1.0) N))
66.0ms	(sqrt (/ (+ N 1.0) N))
167.0ms	(log (sqrt (/ (+ N 1.0) N)))
176.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify1.2s

Counts

130 → 130

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	123	45078
1	202	39652
2	474	38368
3	1644	38368
done	5001	38288

prune730.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

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))))

rewrite48.0ms

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×	`add-cbrt-cube` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `log-div` `rem-log-exp`

Counts

4 → 137

Calls

4 calls:

13.0ms	(sqrt (sqrt (/ (+ N 1.0) N)))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
12.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

series765.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (sqrt (/ (+ N 1.0) N)))
160.0ms	(log (sqrt (/ (+ N 1.0) N)))
218.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
258.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

simplify2.3s

Counts

149 → 149

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	215	62202
1	346	54963
2	803	53637
3	2993	53517
done	5000	53437

prune794.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes58.0ms

Accuracy

100% (0.0b remaining)

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

bsearch36.0ms

Steps

Iters	Range		Point
7	160.65039477392645	5787.9300826946865	5705.4022801559

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	905
1	28	905
done	28	905

end0.0ms

sample2.8s

Algorithm

intervals

Results

867.0ms	7946×	body	80	nan
718.0ms	1783×	body	1280	valid
413.0ms	1303×	body	640	valid
318.0ms	4055×	body	80	valid
122.0ms	557×	body	320	valid
32.0ms	302×	body	160	valid