Details

Time bar (total: 18.8s)

sample63.0ms

Algorithm
intervals
Results
18.0ms55×body1280valid
9.0ms46×body640valid
9.0ms252×body80nan
7.0ms125×body80valid
2.0ms17×body320valid
1.0ms13×body160valid

simplify9.0ms

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: 30.7b

localize9.0ms

Local error

Found 2 expressions with local error:

3.2b
(- (log (+ N 1.0)) (log N))
4.1b
(log (+ N 1.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
16.0ms
(- (log (+ N 1.0)) (log N))
19.0ms
(log (+ N 1.0))

series181.0ms

Counts
2 → 6
Calls
2 calls:
123.0ms
(- (log (+ N 1.0)) (log N))
57.0ms
(log (+ N 1.0))

simplify3.3s

Counts
71 → 71
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01271052
1277855
2668705
32055614
done5000592

prune171.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1.0 (/ 0.5 N))
0.0b
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
0.3b
(/ 0.3333333333333333 (pow N 3))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
65×*-un-lft-identity
64×times-frac
63×add-cube-cbrt
39×prod-diff
12×unpow-prod-down cube-prod associate-/r*
8×add-exp-log
5×add-cbrt-cube add-log-exp
4×cube-mult unpow3 div-inv sqr-pow
3×pow1 expm1-log1p-u fma-neg div-exp log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num flip-- fma-udef distribute-lft-out--
Counts
3 → 136
Calls
3 calls:
28.0ms
(- 1.0 (/ 0.5 N))
1.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
20.0ms
(/ 0.3333333333333333 (pow N 3))

series171.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(- 1.0 (/ 0.5 N))
77.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
50.0ms
(/ 0.3333333333333333 (pow N 3))

simplify1.7s

Counts
145 → 145
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02642717
15562339
215031778
done50001368

prune346.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
0.2b
(pow (/ 0.5 N) 3)
0.3b
(/ 0.3333333333333333 (pow N 3))
17.6b
(/ (- (pow 1.0 3) (pow (/ 0.5 N) 3)) (fma 1.0 1.0 (* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
279×add-sqr-sqrt
195×times-frac
132×*-un-lft-identity
97×unpow-prod-down cube-prod
96×difference-of-squares
90×add-cube-cbrt
45×sqr-pow
36×associate-/l*
20×distribute-lft-out--
19×add-exp-log
16×add-cbrt-cube
15×associate-/r*
13×associate-*l*
7×pow1
6×div-exp
5×cube-mult unpow3 div-inv
4×difference-cubes cbrt-undiv expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-unpow pow-exp
2×frac-times pow-to-exp frac-2neg flip3-+ associate-*r/ prod-exp clear-num cbrt-unprod flip-+ associate-/l/ rem-cube-cbrt unswap-sqr
1×cube-div distribute-rgt-in flip3-- pow-pow distribute-lft-in div-sub pow-prod-down associate-*l/ *-commutative flip-- distribute-lft-out
Counts
4 → 308
Calls
4 calls:
58.0ms
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
9.0ms
(pow (/ 0.5 N) 3)
15.0ms
(/ 0.3333333333333333 (pow N 3))
243.0ms
(/ (- (pow 1.0 3) (pow (/ 0.5 N) 3)) (fma 1.0 1.0 (* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
72.0ms
(pow (/ 0.5 N) 3)
66.0ms
(/ 0.3333333333333333 (pow N 3))
295.0ms
(/ (- (pow 1.0 3) (pow (/ 0.5 N) 3)) (fma 1.0 1.0 (* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))))

simplify3.5s

Counts
320 → 320
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
04158156
110467638
244187390
done50007390

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
0.2b
(pow (/ 0.5 N) 3)
0.2b
(pow (/ 0.5 N) 3)
0.3b
(/ 0.3333333333333333 (pow N 3))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
82×times-frac
72×add-sqr-sqrt
69×*-un-lft-identity
67×add-cube-cbrt
38×unpow-prod-down cube-prod
20×add-exp-log
17×add-cbrt-cube
13×associate-*l*
12×associate-/r*
8×pow1
6×cube-mult pow-unpow unpow3 div-exp div-inv sqr-pow
5×pow-exp
4×cbrt-undiv expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp rem-cube-cbrt
3×pow-to-exp associate-/l*
2×cube-div frac-times pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ unswap-sqr
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num *-commutative distribute-lft-out
Counts
4 → 204
Calls
4 calls:
81.0ms
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
13.0ms
(pow (/ 0.5 N) 3)
11.0ms
(pow (/ 0.5 N) 3)
15.0ms
(/ 0.3333333333333333 (pow N 3))

series316.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (/ 0.5 N) (+ 1.0 (/ 0.5 N)))
59.0ms
(pow (/ 0.5 N) 3)
65.0ms
(pow (/ 0.5 N) 3)
52.0ms
(/ 0.3333333333333333 (pow N 3))

simplify2.6s

Counts
216 → 216
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02332346
16652012
231091841
done50001840

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

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

bsearch49.0ms

Steps
ItersRangePoint
6
9556.682540875734
100426.34546533476
9772.093561518632

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02653
13153
done3153

end0.0ms

sample2.7s

Algorithm
intervals
Results
957.0ms1714×body1280valid
440.0ms8150×body80nan
408.0ms1276×body640valid
307.0ms4126×body80valid
150.0ms591×body320valid
33.0ms293×body160valid