Details

Time bar (total: 32.6s)

sample90.0ms

Algorithm
intervals
Results
28.0ms52×body1280valid
17.0ms50×body640valid
16.0ms277×body80nan
12.0ms125×body80valid
4.0ms20×body320valid
1.0ms9×body160valid

simplify10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite428.0ms

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
424.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series82.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(- (log (+ N 1)) (log N))
25.0ms
(log (+ N 1))

simplify1.6s

Counts
29 → 49
Calls
29 calls:
Slowest
334.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
226.0ms
(- (+ (* 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)))
193.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
178.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune377.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

10.8b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.3b
(/ 1/3 (* N N))
0.3b
(/ -1/2 (* N N))
0.3b
(+ (/ 1 N) (/ -1/2 (* N N)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×add-cbrt-cube add-exp-log
11×add-log-exp
8×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
6×times-frac associate-/l*
5×frac-add
4×pow1 cbrt-undiv sum-log div-exp insert-posit16 div-inv
3×flip3-+ flip-+
2×+-commutative clear-num associate-/r* frac-2neg prod-exp cbrt-unprod
1×associate-+l+
Counts
4 → 79
Calls
4 calls:
Slowest
110.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
17.0ms
(+ (/ 1 N) (/ -1/2 (* N N)))
7.0ms
(/ 1/3 (* N N))
7.0ms
(/ -1/2 (* N N))

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(+ (/ 1 N) (/ -1/2 (* N N)))
51.0ms
(/ -1/2 (* N N))
45.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
32.0ms
(/ 1/3 (* N N))

simplify4.9s

Counts
53 → 91
Calls
53 calls:
Slowest
456.0ms
(- (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))) (* 1/2 (/ 1 (pow N 2))))
379.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
376.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
347.0ms
(/ (* (* 1/3 1/3) 1/3) (* (* (* N N) N) (* (* N N) N)))
339.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))

prune796.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

26.5b
(/ (* -1/2 N) (* N N))
12.7b
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
2.6b
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1/3 (* N N)) (+ 1 (/ (* -1/2 N) (* N N))))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
0.3b
(/ 1/3 (* N N))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
35×add-cbrt-cube add-exp-log
24×add-sqr-sqrt
19×associate-/l/
13×*-un-lft-identity
12×frac-times times-frac
11×associate-*l*
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×associate-*l/
8×flip3-+ frac-add add-cube-cbrt flip-+
7×flip3-- frac-sub flip--
6×pow1 difference-of-squares
5×associate-/l*
4×associate-*r/ insert-posit16 div-inv add-log-exp
3×clear-num associate-/r* frac-2neg associate-*r* associate-/r/
2×distribute-lft-out--
1×pow-prod-down *-commutative unswap-sqr
Counts
4 → 118
Calls
4 calls:
Slowest
137.0ms
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1/3 (* N N)) (+ 1 (/ (* -1/2 N) (* N N))))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
67.0ms
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
34.0ms
(/ (* -1/2 N) (* N N))
13.0ms
(/ 1/3 (* N N))

series198.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
43.0ms
(/ 1/3 (* N N))
38.0ms
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1/3 (* N N)) (+ 1 (/ (* -1/2 N) (* N N))))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
19.0ms
(/ (* -1/2 N) (* N N))

simplify14.2s

Counts
85 → 130
Calls
85 calls:
Slowest
713.0ms
(* (- (/ 1 N) (/ -1/2 (* N N))) (+ (* 1/3 (+ (* 1 1) (- (* (/ (* -1/2 N) (* N N)) (/ (* -1/2 N) (* N N))) (* 1 (/ (* -1/2 N) (* N N)))))) (* (* N N) (+ (pow 1 3) (pow (/ (* -1/2 N) (* N N)) 3)))))
637.0ms
(* (- (* 1 (* N N)) (* N -1/2)) (+ (/ 1/3 (* N N)) (+ 1 (/ (* -1/2 N) (* N N)))))
633.0ms
(/ (* (* (* -1/2 N) (* -1/2 N)) (* -1/2 N)) (* (* (* N N) (* N N)) (* N N)))
554.0ms
(+ (* (/ 1 N) (/ 1 N)) (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N)))))
526.0ms
(* (* (* (- (/ 1 N) (/ -1/2 (* N N))) (- (/ 1 N) (/ -1/2 (* N N)))) (- (/ 1 N) (/ -1/2 (* N N)))) (* (* N N) N))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

26.0b
(- (exp (log (log (+ N 1)))) (log N))
3.0b
(log (+ N 1))
0.8b
(exp (log (log (+ N 1))))
0.0b
(log (log (+ N 1)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
14×*-un-lft-identity
13×add-sqr-sqrt
10×pow1
9×add-cube-cbrt
6×add-exp-log log-pow
5×exp-sum add-log-exp
4×exp-prod add-cbrt-cube insert-posit16
3×associate--r+
2×log-div rem-log-exp distribute-lft-out-- difference-of-squares
1×sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out rem-exp-log
Counts
4 → 67
Calls
4 calls:
Slowest
36.0ms
(- (exp (log (log (+ N 1)))) (log N))
7.0ms
(log (+ N 1))
6.0ms
(exp (log (log (+ N 1))))
2.0ms
(log (log (+ N 1)))

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(- (exp (log (log (+ N 1)))) (log N))
62.0ms
(log (log (+ N 1)))
36.0ms
(exp (log (log (+ N 1))))
26.0ms
(log (+ N 1))

simplify3.4s

Counts
43 → 79
Calls
43 calls:
Slowest
392.0ms
(- (+ (/ 1 (* (- (log -1) (log (/ -1 N))) N)) (log (- (log -1) (log (/ -1 N))))) (+ (* 1/2 (/ 1 (* (- (log -1) (log (/ -1 N))) (pow N 2)))) (* 1/2 (/ 1 (* (pow (- (log -1) (log (/ -1 N))) 2) (pow N 2))))))
340.0ms
(- (+ (/ 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))))
260.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
244.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))

prune763.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch55.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1752×body1280valid
866.0ms7931×body80nan
494.0ms4083×body80valid
491.0ms1248×body640valid
157.0ms619×body320valid
46.0ms298×body160valid