Details

sample122.0ms

Algorithm

intervals

Results

40.0ms	57×	body	1280	valid
22.0ms	271×	body	80	nan
21.0ms	43×	body	640	valid
16.0ms	129×	body	80	valid
5.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid

simplify10.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

10.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize9.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (log1p N) (log N))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

Slowest

25.0ms

(- (log1p N) (log N))

series67.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

67.0ms

(- (log1p N) (log N))

simplify2.2s

Counts

38 → 40

Calls

38 calls:

Slowest

184.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
175.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
173.0ms	(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
166.0ms	(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
148.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune314.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 66

Calls

2 calls:

Slowest

12.0ms	(/ (+ 1 N) N)
4.0ms	(log (/ (+ 1 N) N))

series115.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

61.0ms	(log (/ (+ 1 N) N))
54.0ms	(/ (+ 1 N) N)

simplify1.9s

Counts

57 → 72

Calls

57 calls:

Slowest

306.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
223.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
214.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
174.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
127.0ms	(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))

prune504.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 130

Calls

4 calls:

Slowest

11.0ms	(sqrt (/ (+ 1 N) N))
11.0ms	(sqrt (/ (+ 1 N) N))
8.0ms	(log (sqrt (/ (+ 1 N) N)))
8.0ms	(log (sqrt (/ (+ 1 N) N)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(log (sqrt (/ (+ 1 N) N)))
75.0ms	(log (sqrt (/ (+ 1 N) N)))
69.0ms	(sqrt (/ (+ 1 N) N))
39.0ms	(sqrt (/ (+ 1 N) N))

simplify2.9s

Counts

96 → 142

Calls

96 calls:

Slowest

245.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
228.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
228.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
213.0ms	(- (+ (* 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

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (log1p N) (log N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

Slowest

6.0ms

(- (log1p N) (log N))

series58.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

58.0ms

(- (log1p N) (log N))

simplify2.3s

Counts

38 → 40

Calls

38 calls:

Slowest

212.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
210.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
191.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
186.0ms	(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
183.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune285.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.6b

bsearch42.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	1759×	body	1280	valid
626.0ms	8063×	body	80	nan
516.0ms	1258×	body	640	valid
440.0ms	4058×	body	80	valid
195.0ms	596×	body	320	valid
54.0ms	329×	body	160	valid