Details

sample76.0ms

Algorithm

intervals

Results

25.0ms	57×	body	1280	valid
13.0ms	271×	body	80	nan
11.0ms	43×	body	640	valid
9.0ms	129×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify21.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize27.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1)) (log N))
1.5b	(log (+ N 1))

rewrite46.0ms

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

38.0ms	(- (log (+ N 1)) (log N))
6.0ms	(log (+ N 1))

series108.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

67.0ms	(- (log (+ N 1)) (log N))
42.0ms	(log (+ N 1))

simplify1.6s

Counts

29 → 49

Calls

29 calls:

Slowest

392.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
189.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
187.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
176.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
159.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune443.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

2.9b	(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

27.0ms	(/ (+ N 1) N)
4.0ms	(log (/ (+ N 1) N))

series120.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

72.0ms	(/ (+ N 1) N)
48.0ms	(log (/ (+ N 1) N))

simplify1.9s

Counts

57 → 68

Calls

57 calls:

Slowest

305.0ms	(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
209.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
184.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
145.0ms	(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
122.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune474.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

2.9b	(log (+ (/ 1 N) 1))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log-prod` `*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt` `distribute-lft-out`
1×	`flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

Slowest

6.0ms

(log (+ (/ 1 N) 1))

series35.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

35.0ms

(log (+ (/ 1 N) 1))

simplify984.0ms

Counts

11 → 20

Calls

11 calls:

Slowest

345.0ms	(log (+ (pow (/ 1 N) 3) (pow 1 3)))
198.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
186.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
110.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
78.0ms	(log (- (* (/ 1 N) (/ 1 N)) (* 1 1)))

prune115.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (sqrt (/ (+ N 1) N)))
2.9b	(log (sqrt (/ (+ N 1) N)))
0.1b	(sqrt (/ (+ N 1) N))
0.1b	(sqrt (/ (+ N 1) N))

rewrite41.0ms

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

14.0ms	(sqrt (/ (+ N 1) N))
10.0ms	(sqrt (/ (+ N 1) N))
7.0ms	(log (sqrt (/ (+ N 1) N)))
6.0ms	(log (sqrt (/ (+ N 1) N)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(log (sqrt (/ (+ N 1) N)))
85.0ms	(log (sqrt (/ (+ N 1) N)))
66.0ms	(sqrt (/ (+ N 1) N))
54.0ms	(sqrt (/ (+ N 1) N))

simplify2.8s

Counts

96 → 134

Calls

96 calls:

Slowest

277.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
217.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
195.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
188.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
155.0ms	(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch48.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	1759×	body	1280	valid
742.0ms	8063×	body	80	nan
485.0ms	1258×	body	640	valid
421.0ms	4058×	body	80	valid
144.0ms	596×	body	320	valid
90.0ms	329×	body	160	valid