Details

Time bar (total: 13.1s)

sample72.0ms

Algorithm
intervals
Results
22.0ms59×body1280valid
11.0ms309×body80nan
11.0ms51×body640valid
8.0ms117×body80valid
4.0ms23×body320valid
1.0ms6×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (log (+ N 1.0)) (log N))
2.9b
(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))

series219.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(- (log (+ N 1.0)) (log N))
86.0ms
(log (+ N 1.0))

simplify3.0s

Counts
47 → 47
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0101510
1213488
2462445
31063443
42574438
done5001426

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (/ 0.5 N)) N)
0.2b
(/ 0.3333333333333333 (pow N 3))
10.8b
(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
59×add-sqr-sqrt
58×*-un-lft-identity
39×add-cube-cbrt
15×associate-/r*
12×unpow-prod-down cube-prod
10×add-exp-log
9×associate-/l*
8×difference-of-squares
7×add-cbrt-cube
5×distribute-lft-out-- add-log-exp
4×cube-mult unpow3 div-exp sqr-pow
3×pow1 distribute-lft-out
2×cbrt-undiv frac-2neg div-sub clear-num div-inv associate-/l/
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ frac-add pow-exp sum-log flip-- flip-+
Counts
3 → 123
Calls
3 calls:
46.0ms
(/ (- 1.0 (/ 0.5 N)) N)
8.0ms
(/ 0.3333333333333333 (pow N 3))
138.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

series230.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (- 1.0 (/ 0.5 N)) N)
58.0ms
(/ 0.3333333333333333 (pow N 3))
58.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

simplify1.2s

Counts
132 → 132
Iterations

Useful iterations: 2 (326.0ms)

IterNodesCost
02031721
14381521
211941426
done50001426

prune424.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (- 1.0 (/ 0.5 N)) (/ 1 N))
0.2b
(/ 0.3333333333333333 (pow N 3))
10.8b
(+ (/ 0.3333333333333333 (pow N 3)) (* (- 1.0 (/ 0.5 N)) (/ 1 N)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt times-frac
39×*-un-lft-identity
36×add-cube-cbrt
17×add-exp-log
13×associate-*r*
12×unpow-prod-down cube-prod associate-/r*
10×add-cbrt-cube
6×associate-*l* frac-add
5×pow1 div-exp add-log-exp
4×cube-mult frac-times flip3-- unpow3 associate-*l/ prod-exp flip-- sqr-pow
3×associate-/l* unswap-sqr
2×cbrt-undiv associate-*r/ un-div-inv cbrt-unprod div-inv difference-of-squares
1×+-commutative pow-to-exp rec-exp frac-2neg flip3-+ 1-exp pow-prod-down pow-exp clear-num sum-log *-commutative flip-+ distribute-lft-out--
Counts
3 → 125
Calls
3 calls:
83.0ms
(* (- 1.0 (/ 0.5 N)) (/ 1 N))
8.0ms
(/ 0.3333333333333333 (pow N 3))
54.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (* (- 1.0 (/ 0.5 N)) (/ 1 N)))

series251.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(* (- 1.0 (/ 0.5 N)) (/ 1 N))
68.0ms
(/ 0.3333333333333333 (pow N 3))
62.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (* (- 1.0 (/ 0.5 N)) (/ 1 N)))

simplify1.4s

Counts
134 → 134
Iterations

Useful iterations: 2 (499.0ms)

IterNodesCost
02351924
15581578
217761442
done50011442

prune386.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.3333333333333333 (pow N 3))
4.1b
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
10.8b
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
17.5b
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×times-frac
32×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down log-prod cube-prod associate-/r*
10×add-exp-log
9×distribute-lft-out
6×pow1 log-div exp-sum add-cbrt-cube add-log-exp
4×cube-mult exp-prod unpow3 sqr-pow
3×flip3-+ exp-diff div-exp frac-add flip-+ associate-/l* distribute-lft-out--
2×log-pow
1×cbrt-undiv +-commutative pow-to-exp associate-+l- frac-2neg div-sub rem-log-exp pow-exp clear-num sum-log div-inv rem-exp-log
Counts
4 → 120
Calls
4 calls:
17.0ms
(/ 0.3333333333333333 (pow N 3))
139.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
174.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
132.0ms
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ 0.3333333333333333 (pow N 3))
51.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
42.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
120.0ms
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

simplify1.0s

Counts
132 → 132
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02132193
14331947
212881740
done50011714

prune412.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch60.0ms

Steps
ItersRangePoint
9
0.00565890190154967
18133.886566758163
3775.8969182145884

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02026
12226
done2226

end0.0ms

sample3.1s

Algorithm
intervals
Results
943.0ms1746×body1280valid
824.0ms8101×body80nan
415.0ms1216×body640valid
307.0ms4125×body80valid
116.0ms614×body320valid
83.0ms299×body160valid