Details

Time bar (total: 3.5s)

sample42.0ms

Algorithm
intervals
Results
15.0ms62×body1280valid
6.0ms40×body640valid
5.0ms122×body80valid
5.0ms226×body80nan
2.0ms22×body320valid
1.0ms10×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: 31.3b

localize6.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (log (+ N 1.0)) (log N))
3.9b
(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))
3.0ms
(log (+ N 1.0))

series136.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(- (log (+ N 1.0)) (log N))
44.0ms
(log (+ N 1.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune101.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite75.0ms

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))
5.0ms
(/ 1 (pow N 2))

series125.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms
(/ 1 (pow N 2))

simplify74.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05831087
12726904
25001841

prune253.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (pow N 2))
18.0b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.0b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.0b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
21×cbrt-div
15×frac-add
13×add-exp-log
12×unpow-prod-down
9×cbrt-prod
8×associate-/r*
6×frac-times flip3-- associate-*r/ div-exp add-cbrt-cube flip--
4×pow1 unpow2 add-log-exp sqr-pow
3×pow-to-exp rec-exp flip3-+ pow1/3 1-exp associate-*l/ pow-exp flip-+ associate-/l*
1×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
Counts
4 → 111
Calls
4 calls:
4.0ms
(/ 1 (pow N 2))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
157.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
154.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
150.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify67.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05141549
120601446
250011388

prune354.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.0b
(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))

series138.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (+ N 1.0) N)
86.0ms
(log (/ (+ N 1.0) N))

simplify106.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0233373
1773351
23489339
35002339

prune111.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

100% (0.0b remaining)

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

bsearch34.0ms

Steps
ItersRangePoint
9
0.08347146558812443
2231369.5462890854
9562.64518051556

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.2s

Algorithm
intervals
Results
417.0ms1787×body1280valid
181.0ms1261×body640valid
178.0ms7984×body80nan
157.0ms4035×body80valid
59.0ms611×body320valid
17.0ms306×body160valid