Details

sample73.0ms

Algorithm

intervals

Results

22.0ms	51×	body	1280	valid
15.0ms	248×	body	80	nan
12.0ms	46×	body	640	valid
9.0ms	132×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	7×	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: 29.2b

localize13.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (log (+ N 1)) (log N))
2.8b	(log (+ N 1))

rewrite19.0ms

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:

13.0ms	(- (log (+ N 1)) (log N))
6.0ms	(log (+ N 1))

series134.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (log (+ N 1)) (log N))
47.0ms	(log (+ N 1))

simplify2.8s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
4	3749
3	1329
2	452
1	200
0	97

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
1.9b	(log (/ (+ N 1) N))

rewrite33.0ms

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:

25.0ms	(/ (+ N 1) N)
6.0ms	(log (/ (+ N 1) N))

series120.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (+ N 1) N)
57.0ms	(log (/ (+ N 1) N))

simplify1.9s

Counts

68 → 68

Iterations

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

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
1.9b	(log (/ (+ 1 N) N))

rewrite29.0ms

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:

20.0ms	(/ (+ 1 N) N)
7.0ms	(log (/ (+ 1 N) N))

series144.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (+ 1 N) N)
63.0ms	(log (/ (+ 1 N) N))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5300
3	2187
2	578
1	233
0	102

prune192.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 N))
0.1b	(/ (sqrt (+ 1 N)) N)
2.2b	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
2.7b	(log (sqrt (+ 1 N)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
39×	`log-prod` `add-cube-cbrt`
25×	`associate-+r+`
14×	`distribute-lft-out`
11×	`pow1`
8×	`sqrt-div`
7×	`associate-+l+` `add-exp-log` `log-pow` `associate-/l*`
6×	`add-cbrt-cube`
5×	`log-div` `flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`sqrt-pow1` `pow1/2` `associate-+l-` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 135

Calls

4 calls:

13.0ms	(sqrt (+ 1 N))
28.0ms	(/ (sqrt (+ 1 N)) N)
41.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
10.0ms	(log (sqrt (+ 1 N)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ 1 N))
72.0ms	(/ (sqrt (+ 1 N)) N)
210.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
99.0ms	(log (sqrt (+ 1 N)))

simplify2.8s

Counts

147 → 147

Iterations

Iter	Nodes
done	5004
3	4618
2	1162
1	454
0	215

prune618.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.8b

bsearch56.0ms

Steps

Iters	Range		Point
8	29.100869698027953	73049.03827748532	8585.191610072276

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	1705×	body	1280	valid
422.0ms	1221×	body	640	valid
419.0ms	4166×	body	80	valid
382.0ms	8127×	body	80	nan
121.0ms	618×	body	320	valid
38.0ms	290×	body	160	valid