Details

Time bar (total: 25.7s)

sample82.0ms

Algorithm
intervals
Results
29.0ms59×body1280valid
13.0ms137×body80valid
12.0ms207×body80nan
11.0ms33×body640valid
5.0ms19×body320valid
1.0ms8×body160valid

simplify20.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize22.0ms

Local error

Found 2 expressions with local error:

3.3b
(log (+ N 1))
1.5b
(- (log (+ N 1)) (log N))

rewrite11.0ms

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
64.0ms
(- (log (+ N 1)) (log N))
23.0ms
(log (+ N 1))

simplify1.8s

Counts
29 → 49
Calls
29 calls:
Slowest
393.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
246.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
243.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
180.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
132.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune490.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

1.8b
(log (/ (+ N 1) N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
15×*-un-lft-identity
12×times-frac
9×add-sqr-sqrt add-cube-cbrt
4×add-exp-log
3×distribute-lft-out
2×pow1 rem-log-exp
1×log-div add-cbrt-cube div-exp log-pow insert-posit16 div-inv add-log-exp
Counts
1 → 28
Calls
1 calls:
Slowest
4.0ms
(log (/ (+ N 1) N))

series62.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
62.0ms
(log (/ (+ N 1) N))

simplify1.0s

Counts
22 → 31
Calls
22 calls:
Slowest
201.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
157.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
122.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
115.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
76.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) 1))

prune244.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

15.4b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.3b
(/ 1/3 (* N N))
0.2b
(/ -1/2 (* N N))
0.1b
(/ (/ 1/3 (* N N)) N)

rewrite159.0ms

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
128.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
13.0ms
(/ (/ 1/3 (* N N)) N)
10.0ms
(/ 1/3 (* N N))
6.0ms
(/ -1/2 (* N N))

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
50.0ms
(/ 1/3 (* N N))
45.0ms
(/ (/ 1/3 (* N N)) N)
42.0ms
(/ -1/2 (* N N))
36.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))

simplify6.7s

Counts
103 → 125
Calls
103 calls:
Slowest
477.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
453.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
350.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
330.0ms
(/ (* (* 1/3 1/3) 1/3) (* (* (* N N) N) (* (* N N) N)))
328.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

23.3b
(log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N)))
15.4b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
3.6b
(exp (log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))))
0.3b
(/ 1/3 (* N N))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
15×distribute-lft-out
12×log-prod frac-add
10×log-div add-exp-log
9×add-sqr-sqrt add-cbrt-cube add-cube-cbrt add-log-exp
6×pow1 flip3-+ exp-sum flip-+
5×exp-diff
4×exp-prod insert-posit16 div-inv
3×sum-log times-frac associate-/l*
2×cbrt-undiv div-exp log-pow
1×+-commutative associate-+l+ clear-num associate-/r* frac-2neg rem-log-exp prod-exp cbrt-unprod rem-exp-log
Counts
4 → 87
Calls
4 calls:
Slowest
89.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
86.0ms
(log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N)))
54.0ms
(exp (log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))))
6.0ms
(/ 1/3 (* N N))

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
54.0ms
(log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N)))
41.0ms
(/ 1/3 (* N N))
36.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
32.0ms
(exp (log (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))))

simplify9.1s

Counts
64 → 99
Calls
64 calls:
Slowest
491.0ms
(log (+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N)))))
454.0ms
(exp (log (+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))))
448.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
424.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
401.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))

prune674.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch66.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
957.0ms7816×body80nan
906.0ms1728×body1280valid
481.0ms4073×body80valid
477.0ms1321×body640valid
134.0ms588×body320valid
77.0ms290×body160valid