Details

sample121.0ms

Algorithm

intervals

Results

51.0ms	54×	body	1280	valid
19.0ms	47×	body	640	valid
19.0ms	273×	body	80	nan
14.0ms	130×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify14.0ms

Calls

1 calls:

Slowest

14.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize17.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (log (+ N 1)) (log N))
2.6b	(log (+ N 1))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

7.0ms	(- (log (+ N 1)) (log N))
1.0ms	(log (+ N 1))

series131.0ms

Calls

2 calls:

Slowest

91.0ms	(- (log (+ N 1)) (log N))
40.0ms	(log (+ N 1))

simplify1.5s

Calls

22 calls:

Slowest

369.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
191.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
179.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
161.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
150.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune370.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

2.8b	(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×	`add-cbrt-cube` `insert-posit16` `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))

series115.0ms

Calls

2 calls:

Slowest

64.0ms	(log (/ (+ N 1) N))
51.0ms	(/ (+ N 1) N)

simplify574.0ms

Calls

16 calls:

Slowest

190.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
142.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
114.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
16.0ms	(+ (/ 1 N) 1)
15.0ms	(log (* (cbrt (/ (+ N 1) N)) (cbrt (/ (+ N 1) N))))

prune270.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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×	`insert-posit16` `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 (+ N 1)) (/ N (sqrt (+ N 1))))
4.0ms	(log (/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1)))))
2.0ms	(/ N (sqrt (+ N 1)))
1.0ms	(sqrt (+ N 1))

series240.0ms

Calls

4 calls:

Slowest

99.0ms	(/ N (sqrt (+ N 1)))
54.0ms	(log (/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1)))))
49.0ms	(/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1))))
38.0ms	(sqrt (+ N 1))

simplify7.1s

Calls

158 calls:

Slowest

269.0ms	(/ (* (* (sqrt (+ N 1)) (sqrt (+ N 1))) (sqrt (+ N 1))) (* (* (/ N (sqrt (+ N 1))) (/ N (sqrt (+ N 1)))) (/ N (sqrt (+ N 1)))))
228.0ms	(log (/ (* (cbrt (sqrt (+ N 1))) (cbrt (sqrt (+ N 1)))) (/ N (sqrt (- (* N N) (* 1 1))))))
191.0ms	(log (/ (* (cbrt (sqrt (+ N 1))) (cbrt (sqrt (+ N 1)))) (/ N (sqrt (+ (pow N 3) (pow 1 3))))))
190.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
184.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

14.2b	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.1b	(/ 1/3 (* N N))
0.1b	(/ -1/2 (* N N))
0.1b	(/ (/ 1/3 (* N N)) N)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `div-inv` `distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `frac-add` `add-exp-log` `insert-posit16` `associate-/l*`
3×	`clear-num` `sum-log` `frac-2neg`
2×	`associate-/r*` `flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-/l/`

Calls

4 calls:

Slowest

49.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
7.0ms	(/ (/ 1/3 (* N N)) N)
1.0ms	(/ 1/3 (* N N))
1.0ms	(/ -1/2 (* N N))

series151.0ms

Calls

4 calls:

Slowest

49.0ms	(/ (/ 1/3 (* N N)) N)
38.0ms	(/ 1/3 (* N N))
36.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
28.0ms	(/ -1/2 (* N N))

simplify2.4s

Calls

26 calls:

Slowest

520.0ms	(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
364.0ms	(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
237.0ms	(+ (* (+ (pow (/ 1 N) 3) (pow (/ -1/2 (* N N)) 3)) N) (* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) (/ 1/3 (* N N))))
189.0ms	(+ (* (+ (* 1 (* N N)) (* N -1/2)) N) (* (* N (* N N)) (/ 1/3 (* N N))))
175.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune626.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

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

bsearch56.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	1702×	body	1280	valid
862.0ms	1320×	body	640	valid
544.0ms	8046×	body	80	nan
440.0ms	4043×	body	80	valid
157.0ms	616×	body	320	valid
48.0ms	319×	body	160	valid