Details

Time bar (total: 4.8s)

sample47.0ms

Algorithm
intervals
Results
14.0ms57×body1280valid
8.0ms53×body640valid
6.0ms267×body80nan
5.0ms118×body80valid
2.0ms20×body320valid
0.0ms8×body160valid

simplify8.0ms

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: 32.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(log (+ N 1.0))
2.5b
(- (log (+ N 1.0)) (log N))

rewrite17.0ms

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:
4.0ms
(log (+ N 1.0))
12.0ms
(- (log (+ N 1.0)) (log N))

series135.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(log (+ N 1.0))
95.0ms
(- (log (+ N 1.0)) (log N))

simplify58.0ms

Counts
47 → 47
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0212281
1547264
21875250
35001247
done5001247

prune99.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

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))
0.9b
(/ 1 (pow N 2))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
57×times-frac
42×*-un-lft-identity
36×add-cube-cbrt
32×add-exp-log
28×associate-*l*
23×unpow-prod-down
12×div-exp
10×prod-exp add-cbrt-cube
9×unpow2 unswap-sqr sqr-pow
8×associate-/r*
6×pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×pow1 frac-add add-log-exp
4×distribute-rgt-in frac-times sub-neg associate-+l+ flip3-- distribute-lft-in associate-*r/ flip--
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod div-inv difference-of-squares
1×+-commutative pow-flip frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ distribute-lft-out-- inv-pow
Counts
3 → 150
Calls
3 calls:
29.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
64.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
11.0ms
(/ 1 (pow N 2))

series129.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
72.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
20.0ms
(/ 1 (pow N 2))

simplify70.0ms

Counts
159 → 159
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05831087
12726904
25001841
done5001841

prune255.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (pow N 2))
3.1b
(/ (+ (* (* (/ 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)))))
11.6b
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
16.6b
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

rewrite864.0ms

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))
580.0ms
(/ (+ (* (* (/ 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)))))
54.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
211.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

series277.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
106.0ms
(/ (+ (* (* (/ 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)))))
44.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
110.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

simplify58.0ms

Counts
201 → 201
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012163170
150012885
done50012885

prune881.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
2.4b
(log (/ (+ N 1.0) 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 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:
21.0ms
(/ (+ N 1.0) N)
6.0ms
(log (/ (+ N 1.0) N))

series134.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (+ N 1.0) N)
87.0ms
(log (/ (+ N 1.0) N))

simplify98.0ms

Counts
66 → 66
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0233373
1773351
23489339
35002339
done5002339

prune105.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch23.0ms

Steps
ItersRangePoint
7
6136.975143603057
736927.0597324986
9607.783785361795

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410
done2410

end0.0ms

sample1.3s

Algorithm
intervals
Results
424.0ms1803×body1280valid
183.0ms1234×body640valid
178.0ms8113×body80nan
162.0ms4021×body80valid
59.0ms634×body320valid
18.0ms308×body160valid