Details

sample79.0ms

Algorithm

intervals

Results

29.0ms	54×	body	1280	valid
11.0ms	270×	body	80	nan
9.0ms	135×	body	80	valid
9.0ms	33×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	13×	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: 28.7b

localize10.0ms

Local error

Found 2 expressions with local error:

3.3b	(log (+ N 1.0))
4.1b	(- (log (+ N 1.0)) (log N))

rewrite16.0ms

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:

4.0ms	(log (+ N 1.0))
10.0ms	(- (log (+ N 1.0)) (log N))

series218.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(log (+ N 1.0))
156.0ms	(- (log (+ N 1.0)) (log N))

simplify1.5s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	1557
2	530
1	213
0	101

prune210.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.9b	(log (/ (+ N 1.0) N))

rewrite25.0ms

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:

16.0ms	(/ (+ N 1.0) N)
5.0ms	(log (/ (+ N 1.0) N))

series232.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(/ (+ N 1.0) N)
131.0ms	(log (/ (+ N 1.0) N))

simplify2.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2289
2	619
1	243
0	108

prune316.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (sqrt (+ N 1.0)) N))
0.1b	(/ (sqrt (+ N 1.0)) N)
3.4b	(log (sqrt (+ N 1.0)))
4.1b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
64×	`log-prod`
63×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-+r+`
16×	`distribute-lft-out`
11×	`pow1`
10×	`add-exp-log`
8×	`log-pow`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `add-cbrt-cube` `sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/r*` `rem-log-exp` `div-inv`
2×	`div-exp` `associate-+l-` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 151

Calls

4 calls:

6.0ms	(log (/ (sqrt (+ N 1.0)) N))
13.0ms	(/ (sqrt (+ N 1.0)) N)
6.0ms	(log (sqrt (+ N 1.0)))
34.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series681.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(log (/ (sqrt (+ N 1.0)) N))
122.0ms	(/ (sqrt (+ N 1.0)) N)
97.0ms	(log (sqrt (+ N 1.0)))
312.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify1.5s

Counts

163 → 163

Iterations

Iter	Nodes
done	5002
2	1378
1	511
0	238

prune792.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (sqrt (+ N 1.0)))
3.4b	(log (sqrt (+ N 1.0)))
4.1b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
4.1b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

78×	`log-prod`
68×	`*-un-lft-identity`
50×	`associate-+r+`
42×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod`
18×	`distribute-lft-out`
16×	`pow1`
14×	`associate-+l+` `log-pow`
10×	`log-div`
8×	`sqrt-div`
6×	`flip3-+` `add-exp-log` `flip-+`
4×	`add-cbrt-cube` `associate-+l-` `add-log-exp`
2×	`+-commutative` `associate-+r-` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `div-inv`

Counts

4 → 140

Calls

4 calls:

8.0ms	(log (sqrt (+ N 1.0)))
6.0ms	(log (sqrt (+ N 1.0)))
20.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
30.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series857.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(log (sqrt (+ N 1.0)))
81.0ms	(log (sqrt (+ N 1.0)))
341.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
323.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify2.9s

Counts

152 → 152

Iterations

Iter	Nodes
done	5002
3	3469
2	903
1	372
0	172

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.7b

bsearch36.0ms

Steps

Iters	Range		Point
9	28.34319947931986	8356907.11246281	9148.879937239351

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample2.4s

Algorithm

intervals

Results

834.0ms	1756×	body	1280	valid
472.0ms	7925×	body	80	nan
334.0ms	1246×	body	640	valid
317.0ms	4031×	body	80	valid
118.0ms	657×	body	320	valid
33.0ms	310×	body	160	valid