Details

Time bar (total: 5.0s)

sample46.0ms

Algorithm
intervals
Results
15.0ms64×body1280valid
6.0ms42×body640valid
6.0ms267×body80nan
5.0ms122×body80valid
2.0ms22×body320valid
0.0ms6×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (log (+ N 1.0)) (log N))
3.4b
(log (+ N 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
5×add-cube-cbrt log-pow
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
12.0ms
(- (log (+ N 1.0)) (log N))
5.0ms
(log (+ N 1.0))

series145.0ms

Counts
2 → 6
Calls
2 calls:
97.0ms
(- (log (+ N 1.0)) (log N))
48.0ms
(log (+ N 1.0))

simplify51.0ms

Counts
47 → 47
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0212281
1547264
21874250
35001247
done5001247

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.0b
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.3b
(/ 1 (pow N 2))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
58×times-frac
45×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*l*
23×unpow-prod-down
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r* add-log-exp
6×pow1 pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×sub-neg flip3-- frac-add flip--
4×distribute-rgt-in frac-times associate-+l+ distribute-lft-in associate-*r/ difference-of-squares
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod div-inv distribute-lft-out--
1×+-commutative pow-flip frac-2neg flip3-+ diff-log pow-prod-down clear-num sum-log *-commutative flip-+ inv-pow
Counts
4 → 165
Calls
4 calls:
19.0ms
(- (/ 0.3333333333333333 N) 0.5)
30.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
67.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
8.0ms
(/ 1 (pow N 2))

series171.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (/ 0.3333333333333333 N) 0.5)
32.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
81.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms
(/ 1 (pow N 2))

simplify71.0ms

Counts
177 → 177
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05971169
12754978
25001915
done5001915

prune298.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow N 2))
2.3b
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
14.4b
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
17.9b
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

rewrite922.0ms

Algorithm
rewrite-expression-head
Rules
108×associate-*l/
82×frac-add
60×associate-*r/
52×add-exp-log
42×associate-/l/
32×frac-times
29×flip3-+ flip-+
28×add-sqr-sqrt
27×times-frac
26×add-cube-cbrt *-un-lft-identity
23×prod-exp
22×add-cbrt-cube
18×flip3-- flip--
14×div-exp
12×unpow-prod-down
11×pow1
9×associate-/r*
8×associate-/r/
7×cbrt-unprod
6×pow-to-exp rec-exp 1-exp associate-*r* pow-exp associate-/l*
4×cbrt-undiv associate-*l* pow-prod-down unpow2 add-log-exp sqr-pow
2×frac-2neg clear-num *-commutative div-inv
1×distribute-rgt-in pow-flip distribute-lft-in inv-pow unswap-sqr
Counts
4 → 189
Calls
4 calls:
8.0ms
(/ 1 (pow N 2))
625.0ms
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
56.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
222.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

series293.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ 1 (pow N 2))
113.0ms
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
40.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
117.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

simplify59.0ms

Counts
201 → 201
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012163170
150012885
done50012885

prune919.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
2.5b
(log (/ (+ N 1.0) N))

rewrite25.0ms

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 div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 60
Calls
2 calls:
17.0ms
(/ (+ N 1.0) N)
6.0ms
(log (/ (+ N 1.0) N))

series142.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (+ N 1.0) N)
88.0ms
(log (/ (+ N 1.0) N))

simplify98.0ms

Counts
66 → 66
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0233373
1773351
23489339
35002339
done5002339

prune106.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.3b

bsearch45.0ms

Steps
ItersRangePoint
9
7.055123656280252
892369.0132880388
9570.307657915993

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04730
14730
done4730

end0.0ms

sample1.3s

Algorithm
intervals
Results
426.0ms1785×body1280valid
186.0ms1260×body640valid
173.0ms7829×body80nan
171.0ms4048×body80valid
61.0ms616×body320valid
17.0ms291×body160valid