Details

Time bar (total: 27.9s)

sample61.0ms

Algorithm
intervals
Results
19.0ms54×body1280valid
10.0ms261×body80nan
10.0ms43×body640valid
9.0ms131×body80valid
3.0ms18×body320valid
1.0ms10×body160valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(- (log (+ N 1)) (log N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 2 expressions with local error:

2.4b
(- (log (+ N 1)) (log N))
2.4b
(log (+ N 1))

rewrite12.0ms

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
Counts
2 → 43
Calls
2 calls:
Slowest
8.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series87.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(- (log (+ N 1)) (log N))
22.0ms
(log (+ N 1))

simplify1.7s

Counts
29 → 49
Calls
29 calls:
Slowest
384.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
265.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
204.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
192.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
175.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune428.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite18.0ms

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-+
Counts
2 → 62
Calls
2 calls:
Slowest
13.0ms
(/ (+ N 1) N)
4.0ms
(log (/ (+ N 1) N))

series137.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
77.0ms
(/ (+ N 1) N)
60.0ms
(log (/ (+ N 1) N))

simplify2.0s

Counts
57 → 68
Calls
57 calls:
Slowest
365.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
218.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
214.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
147.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
101.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune409.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

20.9b
(/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
2.2b
(log (/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
0.1b
(* N (* N N))
0.0b
(* N (+ (* N N) (- (* 1 1) (* N 1))))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
21×pow1
16×add-cbrt-cube
14×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×log-prod
6×times-frac associate-*l* prod-exp associate-*r/
5×pow-prod-up cbrt-unprod
4×flip3-+ div-exp associate-*r* pow-prod-down associate-/r/ flip-+ insert-posit16 add-log-exp
3×rem-log-exp associate-/l*
2×cbrt-undiv *-commutative div-inv unswap-sqr associate-/l/
1×pow2 distribute-rgt-in log-div clear-num associate-/r* frac-2neg distribute-lft-in pow-plus cube-unmult pow-sqr log-pow
Counts
4 → 96
Calls
4 calls:
Slowest
64.0ms
(* N (+ (* N N) (- (* 1 1) (* N 1))))
63.0ms
(/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
28.0ms
(log (/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
14.0ms
(* N (* N N))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
118.0ms
(log (/ (+ 1 (* N (* N N))) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
52.0ms
(* N (* N N))
34.0ms
(* N (+ (* N N) (- (* 1 1) (* N 1))))

simplify9.8s

Counts
70 → 108
Calls
70 calls:
Slowest
637.0ms
(* (* (* N N) N) (* (* (* N N) N) (* (* N N) N)))
570.0ms
(* (* (* N N) N) (* (* (* N N) (* N N)) (* N N)))
565.0ms
(/ (* (* (+ 1 (* N (* N N))) (+ 1 (* N (* N N)))) (+ 1 (* N (* N N)))) (* (* (* N N) N) (* (* (+ (* N N) (- (* 1 1) (* N 1))) (+ (* N N) (- (* 1 1) (* N 1)))) (+ (* N N) (- (* 1 1) (* N 1))))))
564.0ms
(/ (* (* (+ 1 (* N (* N N))) (+ 1 (* N (* N N)))) (+ 1 (* N (* N N)))) (* (* (* N (+ (* N N) (- (* 1 1) (* N 1)))) (* N (+ (* N N) (- (* 1 1) (* N 1))))) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
478.0ms
(log (/ (* (cbrt (+ 1 (* N (* N N)))) (cbrt (+ 1 (* N (* N N))))) N))

prune979.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

13.0b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.6b
(/ 1/3 (* N N))
0.6b
(/ -1/2 (* N N))
0.1b
(/ (/ 1/3 (* N N)) N)

rewrite143.0ms

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/
Counts
4 → 113
Calls
4 calls:
Slowest
109.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
12.0ms
(/ 1/3 (* N N))
11.0ms
(/ (/ 1/3 (* N N)) N)
9.0ms
(/ -1/2 (* N N))

series156.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
46.0ms
(/ (/ 1/3 (* N N)) N)
43.0ms
(/ 1/3 (* N N))
38.0ms
(/ -1/2 (* N N))
30.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))

simplify6.6s

Counts
103 → 125
Calls
103 calls:
Slowest
465.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
337.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
336.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
310.0ms
(+ (* (+ (* 1 (* N N)) (* N -1/2)) N) (* (* N (* N N)) (/ 1/3 (* N N))))
310.0ms
(+ (* (+ (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))))

prune988.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.4b

bsearch70.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.5s1706×body1280valid
596.0ms8167×body80nan
547.0ms1277×body640valid
438.0ms4075×body80valid
160.0ms654×body320valid
47.0ms288×body160valid