Details

Time bar (total: 1.1m)

sample96.0ms

Algorithm
intervals
Results
30.0ms54×body1280valid
17.0ms273×body80nan
17.0ms47×body640valid
13.0ms130×body80valid
4.0ms15×body320valid
2.0ms10×body160valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(- (log (+ N 1)) (log N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×add-sqr-sqrt pow1
5×log-pow add-cube-cbrt
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube 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
19.0ms
(- (log (+ N 1)) (log N))
6.0ms
(log (+ N 1))

series94.0ms

Calls
2 calls:
Slowest
67.0ms
(- (log (+ N 1)) (log N))
27.0ms
(log (+ N 1))

simplify1.7s

Calls
29 calls:
Slowest
411.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
229.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
205.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
177.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
162.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune367.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×div-exp rem-log-exp insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Calls
2 calls:
Slowest
21.0ms
(/ (+ N 1) N)
7.0ms
(log (/ (+ N 1) N))

series110.0ms

Calls
2 calls:
Slowest
61.0ms
(/ (+ N 1) N)
49.0ms
(log (/ (+ N 1) N))

simplify1.9s

Calls
57 calls:
Slowest
323.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
186.0ms
(- (+ (* 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))))
129.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
109.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))

prune488.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

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))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
714×times-frac
552×*-un-lft-identity
420×sqrt-prod
343×add-sqr-sqrt
342×add-cube-cbrt
194×log-prod
105×distribute-lft-out
36×sqrt-div
34×associate-/r* associate-/r/
18×flip3-+ flip-+ div-inv
17×add-exp-log
11×add-cbrt-cube
10×associate-/l*
7×div-exp
6×pow1
4×cbrt-undiv insert-posit16 add-log-exp
3×rem-log-exp
2×clear-num frac-2neg associate-/l/
1×rem-sqrt-square log-div sqrt-pow1 pow1/2 log-pow
Calls
4 calls:
Slowest
32.0ms
(/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1))))
12.0ms
(/ N (sqrt (+ N 1)))
9.0ms
(sqrt (+ N 1))
8.0ms
(log (/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1)))))

series238.0ms

Calls
4 calls:
Slowest
78.0ms
(/ N (sqrt (+ N 1)))
75.0ms
(log (/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1)))))
59.0ms
(/ (sqrt (+ N 1)) (/ N (sqrt (+ N 1))))
25.0ms
(sqrt (+ N 1))

simplify42.2s

Calls
691 calls:
Slowest
648.0ms
(/ (* (* (sqrt (+ N 1)) (sqrt (+ N 1))) (sqrt (+ N 1))) (/ (* (* N N) N) (* (* (sqrt (+ N 1)) (sqrt (+ N 1))) (sqrt (+ N 1)))))
535.0ms
(log (/ (sqrt (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (/ (* (cbrt N) (cbrt N)) (sqrt 1))))
404.0ms
(log (/ (* (cbrt (sqrt (+ N 1))) (cbrt (sqrt (+ N 1)))) (/ (* (cbrt N) (cbrt N)) (* (cbrt (sqrt (+ N 1))) (cbrt (sqrt (+ N 1)))))))
384.0ms
(/ (* (* (sqrt (+ N 1)) (sqrt (+ N 1))) (sqrt (+ N 1))) (* (* (/ N (sqrt (+ N 1))) (/ N (sqrt (+ N 1)))) (/ N (sqrt (+ N 1)))))
367.0ms
(/ (* (* N N) N) (* (* (sqrt (+ N 1)) (sqrt (+ N 1))) (sqrt (+ N 1))))

prune5.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

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)

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
39×times-frac
31×*-un-lft-identity
24×add-sqr-sqrt add-cube-cbrt
23×add-cbrt-cube add-exp-log
13×associate-/l*
9×cbrt-undiv div-exp add-log-exp
8×div-inv
5×associate-/r* distribute-lft-out
4×pow1 frac-add insert-posit16
3×clear-num sum-log frac-2neg prod-exp cbrt-unprod
2×flip3-+ flip-+
1×+-commutative associate-+l+ associate-/l/
Calls
4 calls:
Slowest
114.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
12.0ms
(/ (/ 1/3 (* N N)) N)
6.0ms
(/ -1/2 (* N N))
6.0ms
(/ 1/3 (* N N))

series165.0ms

Calls
4 calls:
Slowest
62.0ms
(/ (/ 1/3 (* N N)) N)
43.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
33.0ms
(/ -1/2 (* N N))
28.0ms
(/ 1/3 (* N N))

simplify6.2s

Calls
103 calls:
Slowest
432.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
359.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
349.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
344.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
298.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))

prune912.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

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

bsearch52.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.1s1702×body1280valid
1.1s1320×body640valid
579.0ms8046×body80nan
466.0ms4043×body80valid
162.0ms616×body320valid
53.0ms319×body160valid