Details

sample89.0ms

Algorithm

intervals

Results

28.0ms	54×	body	1280	valid
17.0ms	47×	body	640	valid
16.0ms	273×	body	80	nan
12.0ms	130×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

11.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize26.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (log1p N) (log N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

1 calls:

Slowest

5.0ms

(- (log1p N) (log N))

series103.0ms

Calls

1 calls:

Slowest

103.0ms

(- (log1p N) (log N))

simplify1.3s

Calls

28 calls:

Slowest

211.0ms	(- (+ (* 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))))
161.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
74.0ms	(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
63.0ms	(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune332.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

2.8b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite10.0ms

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

series120.0ms

Calls

2 calls:

Slowest

63.0ms	(/ (+ 1 N) N)
57.0ms	(log (/ (+ 1 N) N))

simplify721.0ms

Calls

16 calls:

Slowest

215.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
176.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
171.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
27.0ms	(+ (pow 1 3) (pow N 3))
26.0ms	(- (* 1 1) (* N N))

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.4b	(log (/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N)))))
0.2b	(/ N (sqrt (+ 1 N)))
0.0b	(/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N))))
0.0b	(sqrt (+ 1 N))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
41×	`log-prod`
32×	`sqrt-div`
30×	`associate-/r/`
16×	`flip3-+` `flip-+` `div-inv`
12×	`associate-/r*`
9×	`add-exp-log`
6×	`add-cbrt-cube` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-exp` `rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `log-div` `pow1/2` `log-pow`

Calls

4 calls:

Slowest

9.0ms	(/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N))))
4.0ms	(log (/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N)))))
1.0ms	(/ N (sqrt (+ 1 N)))
1.0ms	(sqrt (+ 1 N))

series266.0ms

Calls

4 calls:

Slowest

102.0ms	(/ N (sqrt (+ 1 N)))
71.0ms	(log (/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N)))))
69.0ms	(/ (sqrt (+ 1 N)) (/ N (sqrt (+ 1 N))))
23.0ms	(sqrt (+ 1 N))

simplify6.8s

Calls

158 calls:

Slowest

308.0ms	(- (+ N (* 3/8 (pow N 3))) (* 1/2 (pow N 2)))
250.0ms	(/ (* (* (sqrt (+ 1 N)) (sqrt (+ 1 N))) (sqrt (+ 1 N))) (* (* (/ N (sqrt (+ 1 N))) (/ N (sqrt (+ 1 N)))) (/ N (sqrt (+ 1 N)))))
210.0ms	(log (/ (* (cbrt (sqrt (+ 1 N))) (cbrt (sqrt (+ 1 N)))) (/ N (sqrt (- (* 1 1) (* N N))))))
196.0ms	(- (+ (* 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))))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1/3 N)
0.1b	(/ 1 (* N N))
0.1b	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))

rewrite2.0ms

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

1.0ms	(/ 1 (* N N))
0.0ms	(/ 1/3 N)
0.0ms	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))

series70.0ms

Calls

3 calls:

Slowest

29.0ms	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))
22.0ms	(/ 1/3 N)
18.0ms	(/ 1 (* N N))

simplify666.0ms

Calls

11 calls:

Slowest

214.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
201.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
198.0ms	(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
13.0ms	(/ 1 (pow N 2))
11.0ms	(/ 1 (pow N 2))

prune368.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch50.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

964.0ms	1702×	body	1280	valid
946.0ms	8046×	body	80	nan
586.0ms	1320×	body	640	valid
419.0ms	4043×	body	80	valid
142.0ms	616×	body	320	valid
47.0ms	319×	body	160	valid