Details

Time bar (total: 5.1s)

sample59.0ms

Algorithm
intervals
Results
17.0ms59×body1280valid
11.0ms254×body80nan
10.0ms126×body80valid
9.0ms44×body640valid
2.0ms16×body320valid
1.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b
(- (log (+ N 1.0)) (log N))
2.7b
(log (+ N 1.0))

rewrite10.0ms

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:
6.0ms
(- (log (+ N 1.0)) (log N))
2.0ms
(log (+ N 1.0))

series134.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (log (+ N 1.0)) (log N))
44.0ms
(log (+ N 1.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune103.0ms

Pruning

3 alts after pruning (3 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))
0.4b
(/ 1 (pow N 2))

rewrite74.0ms

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:
18.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
46.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms
(/ 1 (pow N 2))

series122.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms
(/ 1 (pow N 2))

simplify78.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05831087
12726904
25001841

prune261.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (pow N 2))
1.9b
(/ (+ (* (* (/ 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))))
15.8b
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

rewrite699.0ms

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:
4.0ms
(/ 1 (pow N 2))
478.0ms
(/ (+ (* (* (/ 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)))))
34.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
169.0ms
(* (* (/ 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))
114.0ms
(/ (+ (* (* (/ 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)))))
38.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))
109.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)

simplify64.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
012163170
150012885

prune904.0ms

Pruning

5 alts after pruning (4 fresh and 1 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))

rewrite13.0ms

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:
8.0ms
(/ (+ N 1.0) N)
4.0ms
(log (/ (+ N 1.0) N))

series135.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ (+ N 1.0) N)
84.0ms
(log (/ (+ N 1.0) N))

simplify98.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0233373
1773351
23489339
35002339

prune106.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch37.0ms

Steps
ItersRangePoint
8
0.24914757354793585
14520.350903362307
9218.498313538437

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample1.7s

Algorithm
intervals
Results
537.0ms1806×body1280valid
337.0ms8128×body80nan
316.0ms4086×body80valid
238.0ms1205×body640valid
80.0ms577×body320valid
33.0ms326×body160valid