Details

Time bar (total: 16.0s)

sample87.0ms

Algorithm
intervals
Results
26.0ms55×body1280valid
14.0ms46×body640valid
12.0ms252×body80nan
10.0ms125×body80valid
4.0ms17×body320valid
2.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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:
29.0ms
(- (log (+ N 1.0)) (log N))
16.0ms
(log (+ N 1.0))

series187.0ms

Counts
2 → 6
Calls
2 calls:
119.0ms
(- (log (+ N 1.0)) (log N))
68.0ms
(log (+ N 1.0))

simplify4.0s

Counts
71 → 71
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01271052
1277855
2668705
32055614
done5000592

prune222.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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))

rewrite64.0ms

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:
25.0ms
(- 1.0 (/ 0.5 N))
1.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
19.0ms
(/ 0.3333333333333333 (pow N 3))

series221.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(- 1.0 (/ 0.5 N))
78.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
78.0ms
(/ 0.3333333333333333 (pow N 3))

simplify1.6s

Counts
145 → 145
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02642717
15562339
215031778
done50001368

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (/ 1 N) (cbrt (pow (- 1.0 (/ 0.5 N)) 3)) (/ 0.3333333333333333 (pow N 3)))
0.2b
(pow (- 1.0 (/ 0.5 N)) 3)
0.3b
(/ 0.3333333333333333 (pow N 3))
16.9b
(cbrt (pow (- 1.0 (/ 0.5 N)) 3))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
43×*-un-lft-identity
40×times-frac
35×add-cube-cbrt
24×unpow-prod-down cube-prod
18×cbrt-prod
12×associate-/r*
10×add-exp-log
8×difference-of-squares
7×add-cbrt-cube
6×cube-mult unpow3 sqr-pow
5×pow1
4×cube-div expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-unpow div-exp associate-/l*
2×pow-to-exp cbrt-div flip3-- pow-exp flip--
1×cbrt-undiv pow-pow frac-2neg pow1/3 clear-num rem-cbrt-cube fma-udef div-inv rem-cube-cbrt
Counts
4 → 141
Calls
4 calls:
0.0ms
(fma (/ 1 N) (cbrt (pow (- 1.0 (/ 0.5 N)) 3)) (/ 0.3333333333333333 (pow N 3)))
26.0ms
(pow (- 1.0 (/ 0.5 N)) 3)
15.0ms
(/ 0.3333333333333333 (pow N 3))
31.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3))

series228.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma (/ 1 N) (cbrt (pow (- 1.0 (/ 0.5 N)) 3)) (/ 0.3333333333333333 (pow N 3)))
47.0ms
(pow (- 1.0 (/ 0.5 N)) 3)
55.0ms
(/ 0.3333333333333333 (pow N 3))
61.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3))

simplify1.0s

Counts
153 → 153
Iterations

Useful iterations: done (999.0ms)

IterNodesCost
02122019
14481623
213561485
done50001479

prune548.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)) (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)))
0.0b
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
0.0b
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
0.3b
(/ 0.3333333333333333 (pow N 3))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
88×cbrt-prod
63×*-un-lft-identity
60×unpow-prod-down
45×add-cube-cbrt
42×times-frac
18×sqr-pow
16×unswap-sqr
15×swap-sqr
13×associate-*r* associate-*l*
12×cube-prod associate-/r* difference-of-squares
11×pow1 add-exp-log
8×pow1/3 distribute-lft-out--
6×add-cbrt-cube
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×div-exp associate-/l*
2×pow-prod-down pow-sqr pow-prod-up
1×cbrt-undiv pow2 pow-to-exp frac-2neg pow-plus pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 184
Calls
4 calls:
257.0ms
(* (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)) (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)))
43.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
23.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
9.0ms
(/ 0.3333333333333333 (pow N 3))

series229.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)) (cbrt (pow (- 1.0 (/ 0.5 N)) 3/2)))
58.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
63.0ms
(cbrt (pow (- 1.0 (/ 0.5 N)) 3/2))
46.0ms
(/ 0.3333333333333333 (pow N 3))

simplify2.9s

Counts
196 → 196
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02313419
14023045
210612913
341112728
done50002718

prune841.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

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

bsearch30.0ms

Steps
ItersRangePoint
6
9556.682540875734
100426.34546533476
9772.093561518632

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02236
12536
done2536

end0.0ms

sample2.9s

Algorithm
intervals
Results
814.0ms1276×body640valid
738.0ms1714×body1280valid
488.0ms8150×body80nan
324.0ms4126×body80valid
106.0ms591×body320valid
38.0ms293×body160valid