Details

Time bar (total: 13.1s)

sample121.0ms

Algorithm
intervals
Results
42.0ms55×body1280valid
20.0ms269×body80nan
19.0ms41×body640valid
15.0ms129×body80valid
6.0ms20×body320valid
2.0ms11×body160valid

simplify21.0ms

Calls
1 calls:
Slowest
20.0ms
(- (log (+ N 1)) (log N))

prune8.0ms

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))

rewrite14.0ms

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

series108.0ms

Calls
2 calls:
Slowest
68.0ms
(- (log (+ N 1)) (log N))
40.0ms
(log (+ N 1))

simplify1.4s

Calls
22 calls:
Slowest
403.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
187.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
154.0ms
(- (+ (* 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))))
140.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune362.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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
6.0ms
(/ (+ N 1) N)
2.0ms
(log (/ (+ N 1) N))

series89.0ms

Calls
2 calls:
Slowest
55.0ms
(log (/ (+ N 1) N))
33.0ms
(/ (+ N 1) N)

simplify587.0ms

Calls
16 calls:
Slowest
175.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
171.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
104.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
24.0ms
(- (* N N) (* 1 1))
13.0ms
(+ (/ 1 N) 1)

prune296.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

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)))

rewrite22.0ms

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×insert-posit16 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
15.0ms
(* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N))))
3.0ms
(sqrt (log (/ (+ N 1) N)))
1.0ms
(log (/ (+ N 1) N))
1.0ms
(log (/ (+ N 1) N))

series188.0ms

Calls
4 calls:
Slowest
56.0ms
(sqrt (log (/ (+ N 1) N)))
52.0ms
(log (/ (+ N 1) N))
43.0ms
(log (/ (+ N 1) N))
36.0ms
(* (sqrt (log (/ (+ N 1) N))) (sqrt (log (/ (+ N 1) N))))

simplify2.9s

Calls
53 calls:
Slowest
252.0ms
(* (* (* (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)))))
244.0ms
(- (+ (* 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)))))))
203.0ms
(- (+ (* 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))))
179.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune609.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.0b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.7b
(/ 1/3 (* N N))
0.7b
(/ -1/2 (* N N))
0.1b
(/ (/ 1/3 (* N N)) N)

rewrite33.0ms

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
28.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
3.0ms
(/ (/ 1/3 (* N N)) N)
0.0ms
(/ 1/3 (* N N))
0.0ms
(/ -1/2 (* N N))

series74.0ms

Calls
4 calls:
Slowest
24.0ms
(/ (/ 1/3 (* N N)) N)
18.0ms
(/ -1/2 (* N N))
18.0ms
(/ 1/3 (* N N))
14.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))

simplify2.3s

Calls
26 calls:
Slowest
408.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
294.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
292.0ms
(+ (* (+ (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))))
241.0ms
(+ (* (+ (* 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))))

prune495.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

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

bsearch41.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
989.0ms1745×body1280valid
928.0ms8068×body80nan
537.0ms1245×body640valid
392.0ms4092×body80valid
145.0ms609×body320valid
47.0ms309×body160valid