Details

sample71.0ms

Algorithm

intervals

Results

22.0ms	55×	body	1280	valid
12.0ms	269×	body	80	nan
11.0ms	41×	body	640	valid
9.0ms	129×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify17.0ms

Calls

1 calls:

Slowest

17.0ms

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize22.0ms

Local error

Found 2 expressions with local error:

3.8b	(log (+ N 1))
2.4b	(- (log (+ N 1)) (log N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`prod-diff` `add-cube-cbrt`
8×	`pow1`
6×	`log-prod` `log-pow`
4×	`log-div` `fma-neg`
3×	`associate--l+` `add-exp-log`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Calls

2 calls:

Slowest

12.0ms	(- (log (+ N 1)) (log N))
2.0ms	(log (+ N 1))

series91.0ms

Calls

2 calls:

Slowest

64.0ms	(- (log (+ N 1)) (log N))
27.0ms	(log (+ N 1))

simplify2.4s

Calls

48 calls:

Slowest

375.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
247.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
164.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
162.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
143.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune491.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`log-div` `clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `log-pow` `flip-+`

Calls

2 calls:

Slowest

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

series55.0ms

Calls

2 calls:

Slowest

35.0ms	(log (/ (+ N 1) N))
20.0ms	(/ (+ N 1) N)

simplify663.0ms

Calls

16 calls:

Slowest

193.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
172.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
158.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
27.0ms	(- (* N N) (* 1 1))
14.0ms	(log (* (cbrt (/ (+ N 1) N)) (cbrt (/ (+ N 1) N))))

prune296.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (/ (+ N 1) N))
2.6b	(log (/ (+ N 1) N))
0.3b	(* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N))))
0.1b	(sqrt (log (/ (+ N 1) N)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
12×	`add-sqr-sqrt` `sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`log-prod` `add-exp-log`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube`
5×	`pow1/2` `log-pow`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `rem-log-exp` `pow-prod-down` `pow-prod-up` `div-inv`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

7.0ms	(* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N))))
2.0ms	(sqrt (log (/ (+ N 1) N)))
1.0ms	(log (/ (+ N 1) N))
1.0ms	(log (/ (+ N 1) N))

series188.0ms

Calls

4 calls:

Slowest

57.0ms	(sqrt (log (/ (+ N 1) N)))
53.0ms	(log (/ (+ N 1) N))
39.0ms	(* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N))))
39.0ms	(log (/ (+ N 1) N))

simplify3.0s

Calls

53 calls:

Slowest

320.0ms	(- (+ (* 1/2 (/ N (sqrt (- (log N))))) (sqrt (- (log N)))) (+ (* 1/8 (/ (pow N 2) (pow (sqrt (- (log N))) 3))) (* 1/4 (/ (pow N 2) (sqrt (- (log N)))))))
273.0ms	(* (* (* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N)))) (sqrt (log (/ (+ N 1) N)))) (* (* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N)))) (sqrt (log (/ (+ N 1) N)))))
211.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
199.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
180.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune753.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.7b	(/ 1 (* N N))
0.4b	(/ 1/3 N)
0.1b	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-inv` `pow-flip`
1×	`pow2` `rec-exp` `associate-/r*` `fma-udef` `inv-pow`

Calls

3 calls:

Slowest

2.0ms	(/ 1 (* N N))
0.0ms	(/ 1/3 N)
0.0ms	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))

series51.0ms

Calls

3 calls:

Slowest

26.0ms	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))
13.0ms	(/ 1 (* N N))
11.0ms	(/ 1/3 N)

simplify547.0ms

Calls

11 calls:

Slowest

174.0ms	(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
160.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
152.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
18.0ms	(/ 1 (pow N 2))
11.0ms	(/ 1 (pow N 2))

prune411.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.3b

bsearch65.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1745×	body	1280	valid
556.0ms	1245×	body	640	valid
536.0ms	8068×	body	80	nan
406.0ms	4092×	body	80	valid
150.0ms	609×	body	320	valid
48.0ms	309×	body	160	valid