Details

Time bar (total: 22.1s)

sample79.0ms

Algorithm
intervals
Results
30.0ms56×body1280valid
13.0ms267×body80nan
10.0ms40×body640valid
9.0ms131×body80valid
4.0ms22×body320valid
1.0ms7×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize24.0ms

Local error

Found 2 expressions with local error:

5.2b
(log (+ N 1))
1.7b
(- (log (+ N 1)) (log N))

rewrite24.0ms

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
17.0ms
(- (log (+ N 1)) (log N))
6.0ms
(log (+ N 1))

series99.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
67.0ms
(- (log (+ N 1)) (log N))
32.0ms
(log (+ N 1))

simplify1.8s

Counts
29 → 49
Calls
29 calls:
Slowest
425.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
318.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
220.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
207.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
178.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune393.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

2.1b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite22.0ms

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
14.0ms
(/ (+ N 1) N)
7.0ms
(log (/ (+ N 1) N))

series144.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(/ (+ N 1) N)
70.0ms
(log (/ (+ N 1) N))

simplify1.9s

Counts
57 → 68
Calls
57 calls:
Slowest
314.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
214.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
185.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
127.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
101.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune504.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

5.2b
(log (+ N 1))
5.2b
(log (+ N 1))
5.2b
(log (+ N 1))
1.7b
(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
26×log-prod
21×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
8×associate--l+
7×distribute-rgt-in pow1 distribute-lft-in add-exp-log
6×log-div associate--r+ add-log-exp
5×distribute-lft-out
4×add-cbrt-cube insert-posit16
3×flip3-+ rem-log-exp log-pow flip-+
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
Slowest
12.0ms
(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))
6.0ms
(log (+ N 1))
6.0ms
(log (+ N 1))
6.0ms
(log (+ N 1))

series224.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))
45.0ms
(log (+ N 1))
30.0ms
(log (+ N 1))
29.0ms
(log (+ N 1))

simplify3.9s

Counts
50 → 88
Calls
50 calls:
Slowest
438.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
405.0ms
(- (+ (* 2 (/ (log -1) N)) (+ (/ 1 (pow N 2)) (+ (/ (log (/ -1 N)) (pow N 2)) (* 2/3 (/ (log -1) (pow N 3)))))) (+ (/ 1 (pow N 3)) (+ (* 2/3 (/ (log (/ -1 N)) (pow N 3))) (+ (* 2 (/ (log (/ -1 N)) N)) (/ (log -1) (pow N 2))))))
341.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
320.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
251.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))

prune975.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

10.6b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.6b
(/ 1/3 (* N N))
0.5b
(/ -1/2 (* N N))
0.1b
(/ (/ 1/3 (* N N)) N)

rewrite148.0ms

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
121.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
12.0ms
(/ (/ 1/3 (* N N)) N)
7.0ms
(/ -1/2 (* N N))
7.0ms
(/ 1/3 (* N N))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(/ (/ 1/3 (* N N)) N)
42.0ms
(/ -1/2 (* N N))
38.0ms
(/ 1/3 (* N N))
34.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))

simplify6.7s

Counts
103 → 125
Calls
103 calls:
Slowest
462.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
371.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
347.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
339.0ms
(/ (* (* 1/3 1/3) 1/3) (* (* (* N N) N) (* (* N N) N)))
329.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

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

bsearch47.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.2s1782×body1280valid
877.0ms4087×body80valid
590.0ms7847×body80nan
484.0ms1209×body640valid
192.0ms620×body320valid
77.0ms302×body160valid