Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	60×	body	1280	valid
11.0ms	257×	body	80	nan
9.0ms	39×	body	640	valid
9.0ms	125×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid

simplify25.0ms

Calls

1 calls:

Slowest

25.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize15.0ms

Local error

Found 2 expressions with local error:

3.9b	(- (log (+ N 1)) (log N))
3.2b	(log (+ N 1))

rewrite12.0ms

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

11.0ms	(- (log (+ N 1)) (log N))
1.0ms	(log (+ N 1))

series99.0ms

Calls

2 calls:

Slowest

76.0ms	(- (log (+ N 1)) (log N))
22.0ms	(log (+ N 1))

simplify2.8s

Calls

48 calls:

Slowest

389.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
225.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
223.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
197.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
195.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune552.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (* N N))
0.4b	(/ 1/3 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))

series73.0ms

Calls

3 calls:

Slowest

28.0ms	(fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))
24.0ms	(/ 1/3 N)
20.0ms	(/ 1 (* N N))

simplify628.0ms

Calls

11 calls:

Slowest

217.0ms	(- (+ (* 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))))
169.0ms	(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
15.0ms	(/ 1 (pow N 2))
15.0ms	(/ 1 (pow N 2))

prune466.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

19.9b	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
19.9b	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
19.9b	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
0.5b	(/ 1 (* N N))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series244.0ms

Calls

4 calls:

Slowest

82.0ms	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
74.0ms	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
65.0ms	(cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))
22.0ms	(/ 1 (* N N))

simplify3.5s

Calls

23 calls:

Slowest

327.0ms	(cbrt (sqrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))))
318.0ms	(cbrt (* (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))) (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))))
307.0ms	(cbrt (* (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))) (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))))
294.0ms	(cbrt (* (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))) (cbrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N)))))
270.0ms	(cbrt (sqrt (fma (/ 1 (* N N)) (+ (/ 1/3 N) -1/2) (/ 1 N))))

prune704.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

4.0b	(log (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite5.0ms

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

3.0ms	(/ (+ N 1) N)
1.0ms	(log (/ (+ N 1) N))

series103.0ms

Calls

2 calls:

Slowest

54.0ms	(log (/ (+ N 1) N))
50.0ms	(/ (+ N 1) N)

simplify678.0ms

Calls

16 calls:

Slowest

188.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
181.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
143.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
30.0ms	(- (* N N) (* 1 1))
21.0ms	(+ (pow N 3) (pow 1 3))

prune288.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch41.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	1763×	body	1280	valid
816.0ms	1240×	body	640	valid
585.0ms	8028×	body	80	nan
450.0ms	4103×	body	80	valid
149.0ms	607×	body	320	valid
47.0ms	287×	body	160	valid