Details

sample97.0ms

Algorithm

intervals

Results

30.0ms	54×	body	1280	valid
23.0ms	247×	body	80	nan
12.0ms	131×	body	80	valid
12.0ms	34×	body	640	valid
5.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

(- (log (+ N 1)) (log N))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize11.0ms

Local error

Found 2 expressions with local error:

4.9b	(- (log (+ N 1)) (log N))
2.0b	(log (+ N 1))

rewrite12.0ms

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:

Slowest

8.0ms	(- (log (+ N 1)) (log N))
3.0ms	(log (+ N 1))

series104.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

79.0ms	(- (log (+ N 1)) (log N))
25.0ms	(log (+ N 1))

simplify1.6s

Counts

29 → 49

Calls

29 calls:

Slowest

381.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
185.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
162.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
154.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
139.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune425.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

5.1b	(log (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite32.0ms

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:

Slowest

26.0ms	(/ (+ N 1) N)
5.0ms	(log (/ (+ N 1) N))

series157.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

81.0ms	(/ (+ N 1) N)
76.0ms	(log (/ (+ N 1) N))

simplify1.9s

Counts

57 → 68

Calls

57 calls:

Slowest

344.0ms	(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
251.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
185.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
132.0ms	(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
103.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune495.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b	(log (sqrt (/ (+ N 1) N)))
5.2b	(log (sqrt (/ (+ N 1) N)))
0.1b	(sqrt (/ (+ N 1) N))
0.1b	(sqrt (/ (+ N 1) N))

rewrite24.0ms

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:

Slowest

8.0ms	(log (sqrt (/ (+ N 1) N)))
5.0ms	(sqrt (/ (+ N 1) N))
5.0ms	(sqrt (/ (+ N 1) N))
4.0ms	(log (sqrt (/ (+ N 1) N)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(log (sqrt (/ (+ N 1) N)))
107.0ms	(log (sqrt (/ (+ N 1) N)))
61.0ms	(sqrt (/ (+ N 1) N))
36.0ms	(sqrt (/ (+ N 1) N))

simplify2.7s

Counts

96 → 134

Calls

96 calls:

Slowest

217.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
197.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
196.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
191.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
143.0ms	(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

5.2b	(log (sqrt (/ (+ N 1) N)))
5.1b	(log (/ (+ N 1) N))
0.1b	(sqrt (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite28.0ms

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:

Slowest

13.0ms	(/ (+ N 1) N)
5.0ms	(sqrt (/ (+ N 1) N))
5.0ms	(log (sqrt (/ (+ N 1) N)))
4.0ms	(log (/ (+ N 1) N))

series243.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(log (sqrt (/ (+ N 1) N)))
79.0ms	(/ (+ N 1) N)
44.0ms	(log (/ (+ N 1) N))
40.0ms	(sqrt (/ (+ N 1) N))

simplify3.1s

Counts

105 → 135

Calls

105 calls:

Slowest

283.0ms	(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
229.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
205.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
187.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
168.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch51.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	1793×	body	1280	valid
1.1s	7957×	body	80	nan
500.0ms	1203×	body	640	valid
379.0ms	4072×	body	80	valid
194.0ms	618×	body	320	valid
50.0ms	314×	body	160	valid