Details

sample77.0ms

Algorithm

intervals

Results

25.0ms	55×	body	1280	valid
14.0ms	249×	body	80	nan
11.0ms	139×	body	80	valid
10.0ms	32×	body	640	valid
5.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

Calls

1 calls:

Slowest

15.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize29.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (log1p N) (log N))
0.0b	(log1p N)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
2×	`expm1-log1p-u` `pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

2 calls:

Slowest

6.0ms	(- (log1p N) (log N))
0.0ms	(log1p N)

series101.0ms

Calls

2 calls:

Slowest

79.0ms	(- (log1p N) (log N))
22.0ms	(log1p N)

simplify1.9s

Calls

31 calls:

Slowest

428.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
252.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
189.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
170.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
146.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune311.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

2.3b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite8.0ms

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

5.0ms	(/ (+ 1 N) N)
3.0ms	(log (/ (+ 1 N) N))

series64.0ms

Calls

2 calls:

Slowest

45.0ms	(log (/ (+ 1 N) N))
18.0ms	(/ (+ 1 N) N)

simplify671.0ms

Calls

16 calls:

Slowest

190.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
163.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
152.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
26.0ms	(- (* 1 1) (* N N))
16.0ms	(+ (/ 1 N) 1)

prune325.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (sqrt (/ (+ 1 N) N)))
2.3b	(log (sqrt (/ (+ 1 N) N)))
0.1b	(sqrt (/ (+ 1 N) N))
0.1b	(sqrt (/ (+ 1 N) N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `sqrt-div` `log-pow` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`rem-sqrt-square` `log-div` `rem-log-exp`

Calls

4 calls:

Slowest

3.0ms	(log (sqrt (/ (+ 1 N) N)))
3.0ms	(log (sqrt (/ (+ 1 N) N)))
2.0ms	(sqrt (/ (+ 1 N) N))
2.0ms	(sqrt (/ (+ 1 N) N))

series157.0ms

Calls

4 calls:

Slowest

70.0ms	(log (sqrt (/ (+ 1 N) N)))
41.0ms	(log (sqrt (/ (+ 1 N) N)))
27.0ms	(sqrt (/ (+ 1 N) N))
18.0ms	(sqrt (/ (+ 1 N) N))

simplify1.7s

Calls

42 calls:

Slowest

253.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
191.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
190.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
181.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
138.0ms	(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune752.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (log1p N) (log N))
2.1b	(- (log1p N) (log N))
0.3b	(* (sqrt (- (log1p N) (log N))) (sqrt (- (log1p N) (log N))))
0.1b	(sqrt (- (log1p N) (log N)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`prod-diff`
15×	`sqrt-prod`
14×	`sqrt-div`
9×	`pow1` `flip3--` `flip--`
8×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `add-log-exp`
5×	`pow1/2` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `diff-log` `insert-posit16` `log1p-expm1-u`
2×	`log1p-udef` `sub-neg` `pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

33.0ms	(* (sqrt (- (log1p N) (log N))) (sqrt (- (log1p N) (log N))))
12.0ms	(sqrt (- (log1p N) (log N)))
9.0ms	(- (log1p N) (log N))
6.0ms	(- (log1p N) (log N))

series289.0ms

Calls

4 calls:

Slowest

93.0ms	(sqrt (- (log1p N) (log N)))
78.0ms	(* (sqrt (- (log1p N) (log N))) (sqrt (- (log1p N) (log N))))
61.0ms	(- (log1p N) (log N))
58.0ms	(- (log1p N) (log N))

simplify5.2s

Calls

109 calls:

Slowest

302.0ms	(- (+ (* 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)))))))
241.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
236.0ms	(* (sqrt (- (* (log1p N) (log1p N)) (* (log N) (log N)))) (sqrt (- (log1p N) (log N))))
216.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
211.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch56.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	1713×	body	1280	valid
575.0ms	1276×	body	640	valid
567.0ms	7956×	body	80	nan
432.0ms	4111×	body	80	valid
216.0ms	578×	body	320	valid
53.0ms	322×	body	160	valid