Details

Time bar (total: 43.1s)

sample88.0ms

Algorithm
intervals
Results
28.0ms57×body1280valid
17.0ms288×body80nan
12.0ms136×body80valid
11.0ms33×body640valid
5.0ms23×body320valid
1.0ms7×body160valid

simplify20.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize21.0ms

Local error

Found 2 expressions with local error:

2.9b
(- (log (+ N 1)) (log N))
1.9b
(log (+ N 1))

rewrite40.0ms

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
24.0ms
(log (+ N 1))
15.0ms
(- (log (+ N 1)) (log N))

series92.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
68.0ms
(- (log (+ N 1)) (log N))
24.0ms
(log (+ N 1))

simplify1.6s

Counts
29 → 49
Calls
29 calls:
Slowest
321.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
223.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
198.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
197.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
154.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune796.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite28.0ms

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
23.0ms
(/ (+ N 1) N)
4.0ms
(log (/ (+ N 1) N))

series114.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
67.0ms
(/ (+ N 1) N)
47.0ms
(log (/ (+ N 1) N))

simplify2.0s

Counts
57 → 68
Calls
57 calls:
Slowest
349.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
228.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
186.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
155.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
137.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune500.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))
0.4b
(/ (+ N 1) (sqrt N))
0.2b
(/ 1 (sqrt N))
0.0b
(log (/ 1 (sqrt N)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
102×times-frac
77×add-sqr-sqrt add-cube-cbrt
72×log-prod
57×sqrt-prod
28×associate-+r+
22×associate-+l+
17×distribute-lft-out
15×add-exp-log
13×pow1
12×associate-/r*
9×log-pow
8×add-cbrt-cube
7×associate-/l*
6×pow-flip
5×div-exp div-inv
4×rem-log-exp insert-posit16 add-log-exp
3×log-div
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 1-exp flip-+ inv-pow associate-/l/
1×+-commutative associate-+r- sum-log log-rec associate-+l-
Counts
4 → 204
Calls
4 calls:
Slowest
27.0ms
(/ (+ N 1) (sqrt N))
19.0ms
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))
10.0ms
(/ 1 (sqrt N))
5.0ms
(log (/ 1 (sqrt N)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))
107.0ms
(log (/ 1 (sqrt N)))
89.0ms
(/ (+ N 1) (sqrt N))
52.0ms
(/ 1 (sqrt N))

simplify4.0s

Counts
209 → 216
Calls
209 calls:
Slowest
177.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* (sqrt N) (sqrt N)) (sqrt N)))
138.0ms
(* (/ 1 (sqrt N)) (/ (+ N 1) (sqrt N)))
130.0ms
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))
121.0ms
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))
106.0ms
(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ N 1)))))
0.2b
(/ 1 (/ (sqrt N) (+ N 1)))
0.2b
(/ 1 (sqrt N))
0.1b
(/ (sqrt N) (+ N 1))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
408×times-frac
318×*-un-lft-identity
216×add-sqr-sqrt add-cube-cbrt
120×sqrt-prod
117×log-prod
95×associate-+r+
55×distribute-lft-out
40×associate-/r*
22×associate-+l+
21×add-exp-log
18×associate-/r/
13×pow1 add-cbrt-cube
12×div-inv associate-/l*
10×div-exp
9×flip3-+ flip-+
8×log-pow
6×pow-flip
5×cbrt-undiv
4×log-rec insert-posit16 inv-pow add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
2×log-div
1×+-commutative associate-+r- sum-log sqrt-pow1 pow1/2 unsub-neg associate-+l- distribute-neg-out
Counts
4 → 380
Calls
4 calls:
Slowest
23.0ms
(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ N 1)))))
17.0ms
(/ (sqrt N) (+ N 1))
14.0ms
(/ 1 (/ (sqrt N) (+ N 1)))
10.0ms
(/ 1 (sqrt N))

series492.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ N 1)))))
86.0ms
(/ 1 (/ (sqrt N) (+ N 1)))
85.0ms
(/ (sqrt N) (+ N 1))
47.0ms
(/ 1 (sqrt N))

simplify22.9s

Counts
473 → 392
Calls
473 calls:
Slowest
557.0ms
(/ (* (* 1 1) 1) (/ (* (* (sqrt N) (sqrt N)) (sqrt N)) (* (* (+ N 1) (+ N 1)) (+ N 1))))
433.0ms
(/ (sqrt 1) (/ (sqrt N) (+ (pow N 3) (pow 1 3))))
429.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt N) (+ (pow N 3) (pow 1 3))))
390.0ms
(/ (sqrt 1) (/ (sqrt N) (- (* N N) (* 1 1))))
352.0ms
(/ 1 (/ (sqrt N) (+ (pow N 3) (pow 1 3))))

prune4.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch38.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.1s1744×body1280valid
963.0ms8044×body80nan
515.0ms1261×body640valid
483.0ms4102×body80valid
188.0ms590×body320valid
48.0ms303×body160valid