Details

Time bar (total: 21.4s)

sample92.0ms

Algorithm
intervals
Results
32.0ms60×body1280valid
16.0ms257×body80nan
14.0ms39×body640valid
12.0ms125×body80valid
5.0ms18×body320valid
2.0ms14×body160valid

simplify23.0ms

Calls
1 calls:
Slowest
23.0ms
(- (log (+ N 1)) (log N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize17.0ms

Local error

Found 2 expressions with local error:

3.9b
(- (log (+ N 1)) (log N))
3.2b
(log (+ N 1))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-sqr-sqrt log-prod
4×pow1 log-div add-cube-cbrt
3×associate--l+ add-exp-log
2×associate--l- flip3-+ add-cbrt-cube log-pow flip-+ insert-posit16 distribute-lft-out-- add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Calls
2 calls:
Slowest
6.0ms
(- (log (+ N 1)) (log N))
1.0ms
(log (+ N 1))

series116.0ms

Calls
2 calls:
Slowest
86.0ms
(- (log (+ N 1)) (log N))
30.0ms
(log (+ N 1))

simplify1.3s

Calls
22 calls:
Slowest
323.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
190.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
170.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
145.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
145.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))

prune277.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

13.4b
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.5b
(/ -1/2 (* N N))
0.5b
(/ 1/3 (* N N))
0.1b
(/ (/ 1/3 (* N N)) N)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×add-log-exp
5×add-sqr-sqrt add-cube-cbrt div-inv distribute-lft-out
4×pow1 add-cbrt-cube frac-add add-exp-log insert-posit16 associate-/l*
3×clear-num sum-log frac-2neg
2×associate-/r* flip3-+ flip-+
1×+-commutative associate-+l+ associate-/l/
Calls
4 calls:
Slowest
25.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
3.0ms
(/ (/ 1/3 (* N N)) N)
0.0ms
(/ -1/2 (* N N))
0.0ms
(/ 1/3 (* N N))

series154.0ms

Calls
4 calls:
Slowest
62.0ms
(/ (/ 1/3 (* N N)) N)
35.0ms
(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
31.0ms
(/ 1/3 (* N N))
27.0ms
(/ -1/2 (* N N))

simplify2.3s

Calls
26 calls:
Slowest
449.0ms
(+ (* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N N))))
307.0ms
(* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) N)
271.0ms
(+ (* (+ (pow (/ 1 N) 3) (pow (/ -1/2 (* N N)) 3)) N) (* (+ (* (/ 1 N) (/ 1 N)) (- (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (* (/ 1 N) (/ -1/2 (* N N))))) (/ 1/3 (* N N))))
188.0ms
(+ (* (+ (* 1 (* N N)) (* N -1/2)) N) (* (* N (* N N)) (/ 1/3 (* N N))))
162.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune665.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

32.2b
(/ (* N -1/2) (* N N))
15.8b
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
1.9b
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N)))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
0.5b
(/ -1/2 (* N N))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-/l/
12×frac-times
11×add-cbrt-cube add-exp-log
9×associate-*l/
8×*-un-lft-identity flip3-+ frac-add flip-+
7×add-sqr-sqrt flip3-- frac-sub flip--
6×associate-*l*
5×add-cube-cbrt
4×pow1 associate-*r/ insert-posit16 div-inv add-log-exp
3×cbrt-undiv clear-num associate-/r* frac-2neg div-exp associate-/r/
2×times-frac associate-/l* distribute-lft-out--
1×prod-exp *-commutative cbrt-unprod difference-of-squares
Calls
4 calls:
Slowest
38.0ms
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N)))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
9.0ms
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
3.0ms
(/ (* N -1/2) (* N N))
0.0ms
(/ -1/2 (* N N))

series212.0ms

Calls
4 calls:
Slowest
109.0ms
(* (- (/ 1 N) (/ -1/2 (* N N))) N)
43.0ms
(/ -1/2 (* N N))
37.0ms
(/ (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N)))) (* (- (/ 1 N) (/ -1/2 (* N N))) N))
22.0ms
(/ (* N -1/2) (* N N))

simplify11.0s

Calls
51 calls:
Slowest
1.8s
(/ (* (* (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N)))) (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N))))) (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N))))) (* (* (* (- (/ 1 N) (/ -1/2 (* N N))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) N)) (* (- (/ 1 N) (/ -1/2 (* N N))) N)))
646.0ms
(* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) (+ (pow (+ 1 (/ (* N -1/2) (* N N))) 3) (pow (/ 1/3 (* N N)) 3)))
596.0ms
(* (- (pow (/ 1 N) 3) (pow (/ -1/2 (* N N)) 3)) (+ (* (+ (pow 1 3) (pow (/ (* N -1/2) (* N N)) 3)) (* N N)) (* (+ (* 1 1) (- (* (/ (* N -1/2) (* N N)) (/ (* N -1/2) (* N N))) (* 1 (/ (* N -1/2) (* N N))))) 1/3)))
570.0ms
(- (+ (log (- (/ 1 N) (/ -1/2 (* N N)))) (log (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N))))) (log (* (- (/ 1 N) (/ -1/2 (* N N))) N)))
563.0ms
(* (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ -1/2 (* N N)))) (+ (* (+ (pow 1 3) (pow (/ (* N -1/2) (* N N)) 3)) (* N N)) (* (+ (* 1 1) (- (* (/ (* N -1/2) (* N N)) (/ (* N -1/2) (* N N))) (* 1 (/ (* N -1/2) (* N N))))) 1/3)))

prune888.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

4.0b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt log-prod *-un-lft-identity add-cube-cbrt
3×pow1 add-exp-log associate-/l*
2×add-cbrt-cube insert-posit16 div-inv add-log-exp associate-/l/
1×log-div clear-num frac-2neg flip3-+ rem-log-exp log-pow flip-+
Calls
2 calls:
Slowest
3.0ms
(/ (+ N 1) N)
1.0ms
(log (/ (+ N 1) N))

series111.0ms

Calls
2 calls:
Slowest
69.0ms
(/ (+ N 1) N)
42.0ms
(log (/ (+ N 1) N))

simplify597.0ms

Calls
16 calls:
Slowest
187.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
153.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
103.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
20.0ms
(log (* (cbrt (/ (+ N 1) N)) (cbrt (/ (+ N 1) N))))
19.0ms
(log (sqrt (/ (+ N 1) N)))

prune255.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch46.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1763×body1280valid
516.0ms8028×body80nan
487.0ms1240×body640valid
427.0ms4103×body80valid
152.0ms607×body320valid
75.0ms287×body160valid