Details

sample122.0ms

Algorithm

intervals

Results

38.0ms	55×	body	1280	valid
25.0ms	39×	body	640	valid
19.0ms	251×	body	80	nan
16.0ms	135×	body	80	valid
5.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid

simplify21.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

21.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize18.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (log1p N) (log N))

rewrite14.0ms

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

13.0ms

(- (log1p N) (log N))

series77.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

77.0ms

(- (log1p N) (log N))

simplify2.2s

Counts

38 → 40

Calls

38 calls:

Slowest

198.0ms	(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
193.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
187.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
164.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
151.0ms	(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))

prune385.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite26.0ms

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

18.0ms	(/ (+ 1 N) N)
7.0ms	(log (/ (+ 1 N) N))

series141.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

75.0ms	(/ (+ 1 N) N)
66.0ms	(log (/ (+ 1 N) N))

simplify1.9s

Counts

57 → 72

Calls

57 calls:

Slowest

330.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
229.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
200.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
150.0ms	(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
148.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune516.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

2.0b	(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×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 19

Calls

1 calls:

Slowest

6.0ms

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

series31.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

31.0ms

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

simplify1.1s

Counts

11 → 22

Calls

11 calls:

Slowest

368.0ms	(log (+ (pow (/ 1 N) 3) (pow 1 3)))
219.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
188.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
158.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
108.0ms	(log (- (* (/ 1 N) (/ 1 N)) (* 1 1)))

prune129.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

2.0b	(log (+ (/ 1 N) 1))
0.7b	(exp (log (log (+ (/ 1 N) 1))))
0.0b	(log (log (+ (/ 1 N) 1)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`log-prod`
10×	`*-un-lft-identity`
8×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`add-exp-log` `log-pow`
4×	`exp-prod` `exp-sum`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `rem-log-exp` `distribute-lft-out`
1×	`flip3-+` `flip-+` `div-inv` `rem-exp-log`

Counts

3 → 54

Calls

3 calls:

Slowest

9.0ms	(log (+ (/ 1 N) 1))
6.0ms	(log (log (+ (/ 1 N) 1)))
3.0ms	(exp (log (log (+ (/ 1 N) 1))))

series124.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

52.0ms	(log (log (+ (/ 1 N) 1)))
45.0ms	(exp (log (log (+ (/ 1 N) 1))))
27.0ms	(log (+ (/ 1 N) 1))

simplify2.5s

Counts

31 → 63

Calls

31 calls:

Slowest

319.0ms	(log (+ (pow (/ 1 N) 3) (pow 1 3)))
300.0ms	(- (+ (* 5/24 (/ 1 (pow N 2))) (log (/ 1 N))) (* 1/2 (/ 1 N)))
219.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
208.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
205.0ms	(- (+ (* 1/2 (/ (pow N 2) (log N))) (log (- (log N)))) (+ (/ N (log N)) (* 1/2 (/ (pow N 2) (pow (log N) 2)))))

prune484.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 3.4b

bsearch33.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	1780×	body	1280	valid
1.0s	7972×	body	80	nan
609.0ms	1247×	body	640	valid
475.0ms	4082×	body	80	valid
156.0ms	607×	body	320	valid
47.0ms	284×	body	160	valid