Details

Time bar (total: 30.0s)

sample90.0ms

Algorithm
intervals
Results
31.0ms54×body1280valid
15.0ms36×body640valid
13.0ms137×body80valid
13.0ms209×body80nan
4.0ms18×body320valid
2.0ms11×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (log (+ N 1)) (log N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize24.0ms

Local error

Found 2 expressions with local error:

3.0b
(- (log (+ N 1)) (log N))
2.4b
(log (+ N 1))

rewrite47.0ms

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
40.0ms
(- (log (+ N 1)) (log N))
6.0ms
(log (+ N 1))

series94.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(- (log (+ N 1)) (log N))
29.0ms
(log (+ N 1))

simplify3.0s

Counts
57 → 49
Calls
57 calls:
Slowest
425.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
314.0ms
(* (* (- (log (+ N 1)) (log N)) (- (log (+ N 1)) (log N))) (- (log (+ N 1)) (log N)))
274.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
248.0ms
(- (pow (log (+ N 1)) 3) (pow (log N) 3))
236.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))

prune440.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite17.0ms

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
(/ (+ 1 N) N)
3.0ms
(log (/ (+ 1 N) N))

series107.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
55.0ms
(log (/ (+ 1 N) N))
52.0ms
(/ (+ 1 N) N)

simplify3.7s

Counts
96 → 68
Calls
96 calls:
Slowest
433.0ms
(* (* (/ (+ 1 N) N) (/ (+ 1 N) N)) (/ (+ 1 N) N))
367.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
323.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
271.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
213.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune490.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(log (/ (+ 1 N) N))
3.1b
(log (/ (+ 1 N) N))
0.3b
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
0.1b
(sqrt (log (/ (+ 1 N) N)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×add-sqr-sqrt
32×log-prod
30×sqrt-prod
29×pow1 add-cube-cbrt
24×times-frac
12×add-exp-log
11×swap-sqr
9×sqrt-pow1 pow1/2 log-pow
7×associate-*r* associate-*l*
6×add-cbrt-cube distribute-lft-out
5×pow-prod-up
4×rem-log-exp insert-posit16 add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×log-div div-exp div-inv
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 126
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
8.0ms
(log (/ (+ 1 N) N))
7.0ms
(log (/ (+ 1 N) N))
3.0ms
(sqrt (log (/ (+ 1 N) N)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(sqrt (log (/ (+ 1 N) N)))
69.0ms
(log (/ (+ 1 N) N))
61.0ms
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
53.0ms
(log (/ (+ 1 N) N))

simplify8.0s

Counts
182 → 138
Calls
182 calls:
Slowest
411.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
406.0ms
(- (+ (* 1/2 (/ N (sqrt (- (log N))))) (sqrt (- (log N)))) (+ (* 1/8 (/ (pow N 2) (pow (sqrt (- (log N))) 3))) (* 1/4 (/ (pow N 2) (sqrt (- (log N)))))))
403.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
245.0ms
(* (* (* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N)))) (sqrt (log (/ (+ 1 N) N)))) (* (* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N)))) (sqrt (log (/ (+ 1 N) N)))))
228.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

3.1b
(log (/ (+ 1 N) N))
3.1b
(log (/ (+ 1 N) N))
0.8b
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
0.1b
(sqrt (log (/ (+ 1 N) N)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
37×log-pow
32×pow1 log-prod
27×add-sqr-sqrt
26×add-cube-cbrt
25×exp-prod
24×times-frac
18×distribute-rgt-out
14×distribute-lft-out
11×sqrt-pow1 pow1/2
10×add-exp-log
8×exp-to-pow
5×add-log-exp
4×add-cbrt-cube rem-log-exp sqrt-prod insert-posit16
2×log-div distribute-lft1-in div-exp distribute-rgt1-in div-inv rem-exp-log
1×rem-sqrt-square sum-log exp-sum
Counts
4 → 115
Calls
4 calls:
Slowest
36.0ms
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
4.0ms
(log (/ (+ 1 N) N))
3.0ms
(log (/ (+ 1 N) N))
3.0ms
(sqrt (log (/ (+ 1 N) N)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
85.0ms
(sqrt (log (/ (+ 1 N) N)))
76.0ms
(log (/ (+ 1 N) N))
71.0ms
(log (/ (+ 1 N) N))

simplify6.9s

Counts
150 → 127
Calls
150 calls:
Slowest
474.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
464.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
403.0ms
(- (+ (* 1/2 (/ N (sqrt (- (log N))))) (sqrt (- (log N)))) (+ (* 1/8 (/ (pow N 2) (pow (sqrt (- (log N))) 3))) (* 1/4 (/ (pow N 2) (sqrt (- (log N)))))))
348.0ms
(* (* (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N)))))) (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))) (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N)))))))
279.0ms
(- (+ (pow (sqrt (- (log N))) 2) N) (* 1/2 (pow N 2)))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

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

bsearch36.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1684×body1280valid
591.0ms7809×body80nan
532.0ms1275×body640valid
496.0ms309×body160valid
455.0ms4113×body80valid
154.0ms619×body320valid