Details

sample92.0ms

Algorithm

intervals

Results

29.0ms	57×	body	1280	valid
22.0ms	271×	body	80	nan
14.0ms	43×	body	640	valid
11.0ms	129×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify11.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize11.0ms

Local error

Found 2 expressions with local error:

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

series125.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

102.0ms	(- (log (+ N 1)) (log N))
23.0ms	(log (+ N 1))

simplify1.6s

Counts

29 → 49

Calls

29 calls:

Slowest

378.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
186.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
174.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
174.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
166.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune391.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

2.9b	(log (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite28.0ms

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

23.0ms	(/ (+ N 1) N)
4.0ms	(log (/ (+ N 1) N))

series134.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

90.0ms	(/ (+ N 1) N)
44.0ms	(log (/ (+ N 1) N))

simplify2.0s

Counts

57 → 68

Calls

57 calls:

Slowest

341.0ms	(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
224.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
222.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
156.0ms	(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
100.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune432.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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

12.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

41.0ms

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

simplify1.1s

Counts

11 → 20

Calls

11 calls:

Slowest

422.0ms	(log (+ (pow (/ 1 N) 3) (pow 1 3)))
206.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
183.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
133.0ms	(log (- (* (/ 1 N) (/ 1 N)) (* 1 1)))
126.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune117.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`sqrt-prod`
16×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div` `distribute-lft-out`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 80

Calls

4 calls:

Slowest

21.0ms	(sqrt (+ (/ 1 N) 1))
18.0ms	(sqrt (+ (/ 1 N) 1))
13.0ms	(log (sqrt (+ (/ 1 N) 1)))
12.0ms	(log (sqrt (+ (/ 1 N) 1)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

70.0ms	(log (sqrt (+ (/ 1 N) 1)))
62.0ms	(log (sqrt (+ (/ 1 N) 1)))
22.0ms	(sqrt (+ (/ 1 N) 1))
18.0ms	(sqrt (+ (/ 1 N) 1))

simplify4.0s

Counts

54 → 92

Calls

54 calls:

Slowest

772.0ms	(sqrt (+ (pow (/ 1 N) 3) (pow 1 3)))
458.0ms	(log (sqrt (+ (pow (/ 1 N) 3) (pow 1 3))))
338.0ms	(sqrt (+ (pow (/ 1 N) 3) (pow 1 3)))
316.0ms	(log (sqrt (+ (pow (/ 1 N) 3) (pow 1 3))))
223.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))

prune746.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

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

bsearch48.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	1759×	body	1280	valid
674.0ms	8063×	body	80	nan
541.0ms	1258×	body	640	valid
425.0ms	4058×	body	80	valid
188.0ms	596×	body	320	valid
57.0ms	329×	body	160	valid