Details

Time bar (total: 14.1s)

sample66.0ms

Algorithm
intervals
Results
21.0ms54×body1280valid
11.0ms246×body80nan
11.0ms40×body640valid
8.0ms126×body80valid
4.0ms23×body320valid
1.0ms13×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(- (log (+ N 1)) (log N))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize11.0ms

Local error

Found 2 expressions with local error:

3.4b
(- (log (+ N 1)) (log N))
2.7b
(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
6.0ms
(- (log (+ N 1)) (log N))
1.0ms
(log (+ N 1))

series92.0ms

Calls
2 calls:
Slowest
64.0ms
(- (log (+ N 1)) (log N))
27.0ms
(log (+ N 1))

simplify1.8s

Calls
22 calls:
Slowest
717.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
188.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
173.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
155.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
147.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

12.4b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.3b
(+ (/ 1 N) (/ -1/2 (* N N)))
0.2b
(/ 1/3 (* N N))
0.1b
(/ -1/2 (* N N))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
11×add-log-exp
7×distribute-lft-out
5×frac-add
4×add-sqr-sqrt pow1 sum-log add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 div-inv
3×flip3-+ flip-+
2×+-commutative clear-num associate-/r* frac-2neg
1×associate-+l+
Calls
4 calls:
Slowest
23.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
4.0ms
(+ (/ 1 N) (/ -1/2 (* N N)))
0.0ms
(/ 1/3 (* N N))
0.0ms
(/ -1/2 (* N N))

series74.0ms

Calls
4 calls:
Slowest
37.0ms
(+ (/ 1 N) (/ -1/2 (* N N)))
14.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
13.0ms
(/ 1/3 (* N N))
11.0ms
(/ -1/2 (* N N))

simplify2.5s

Calls
29 calls:
Slowest
415.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
362.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
239.0ms
(+ (* (+ (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))))
217.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
204.0ms
(+ (* (+ (* 1 (* N N)) (* N -1/2)) N) (* (* N (* N N)) (/ 1/3 (* N N))))

prune523.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.6b
(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))

series90.0ms

Calls
2 calls:
Slowest
61.0ms
(log (/ (+ N 1) N))
30.0ms
(/ (+ N 1) N)

simplify610.0ms

Calls
16 calls:
Slowest
168.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
152.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
148.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
24.0ms
(- (* N N) (* 1 1))
13.0ms
(+ (/ 1 N) 1)

prune254.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

17.7b
(- (* (sqrt (log (+ N 1))) (sqrt (log (+ N 1)))) (log N))
2.7b
(log (+ N 1))
2.7b
(log (+ N 1))
0.3b
(* (sqrt (log (+ N 1))) (sqrt (log (+ N 1))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×add-exp-log sqrt-prod
7×associate-*r* associate-*l*
6×log-prod add-cbrt-cube
5×add-log-exp
4×log-div pow1/2 log-pow insert-posit16
2×flip3-+ rem-log-exp pow-prod-down pow-prod-up flip-+
1×pow2 sub-neg rem-square-sqrt pow-plus flip3-- sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod flip-- difference-of-squares
Calls
4 calls:
Slowest
17.0ms
(- (* (sqrt (log (+ N 1))) (sqrt (log (+ N 1)))) (log N))
13.0ms
(* (sqrt (log (+ N 1))) (sqrt (log (+ N 1))))
2.0ms
(log (+ N 1))
2.0ms
(log (+ N 1))

series164.0ms

Calls
4 calls:
Slowest
77.0ms
(- (* (sqrt (log (+ N 1))) (sqrt (log (+ N 1)))) (log N))
36.0ms
(log (+ N 1))
27.0ms
(log (+ N 1))
23.0ms
(* (sqrt (log (+ N 1))) (sqrt (log (+ N 1))))

simplify3.2s

Calls
51 calls:
Slowest
388.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
380.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
365.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
209.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
205.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))

prune912.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.0b

bsearch58.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s1744×body1280valid
620.0ms1247×body640valid
617.0ms7996×body80nan
430.0ms4086×body80valid
148.0ms590×body320valid
52.0ms333×body160valid