Details

Time bar (total: 14.6s)

sample85.0ms

Algorithm
intervals
Results
23.0ms309×body80nan
22.0ms59×body1280valid
11.0ms51×body640valid
8.0ms117×body80valid
3.0ms23×body320valid
1.0ms6×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: 32.8b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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:
14.0ms
(- (log (+ N 1.0)) (log N))
5.0ms
(log (+ N 1.0))

series175.0ms

Counts
2 → 6
Calls
2 calls:
121.0ms
(- (log (+ N 1.0)) (log N))
54.0ms
(log (+ N 1.0))

simplify3.5s

Counts
71 → 71
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01271052
1277855
2668705
32055614
done5000592

prune192.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
0.2b
(/ 0.3333333333333333 (pow N 3))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/r*
7×add-exp-log
4×cube-mult unpow3 add-cbrt-cube sqr-pow
3×div-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num fma-udef div-inv
Counts
2 → 77
Calls
2 calls:
1.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
16.0ms
(/ 0.3333333333333333 (pow N 3))

series92.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
39.0ms
(/ 0.3333333333333333 (pow N 3))

simplify2.6s

Counts
83 → 83
Iterations

Useful iterations: 3 (896.0ms)

IterNodesCost
0122992
1221845
2615774
33466768
done5000768

prune248.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
83×times-frac
74×*-un-lft-identity
49×add-cube-cbrt
22×fma-def
15×associate-/r*
14×difference-of-squares
12×unpow-prod-down cube-prod
10×add-exp-log
9×associate-/l*
8×distribute-lft-out--
7×add-cbrt-cube
5×add-log-exp
4×cube-mult unpow3 div-exp sqr-pow
3×pow1 expm1-log1p-u log1p-expm1-u div-inv distribute-lft-out
2×cbrt-undiv frac-2neg div-sub clear-num associate-/l/
1×+-commutative pow-to-exp associate-+l- flip3-- flip3-+ frac-add pow-exp sum-log flip-- flip-+
Counts
3 → 151
Calls
3 calls:
59.0ms
(/ (- 1.0 (/ 0.5 N)) N)
8.0ms
(/ 0.3333333333333333 (pow N 3))
186.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))

series215.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(/ (- 1.0 (/ 0.5 N)) N)
40.0ms
(/ 0.3333333333333333 (pow N 3))
61.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))

simplify1.0s

Counts
160 → 160
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02091779
14511577
212391487
done50001482

prune526.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

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))))

rewrite520.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
69×times-frac
57×add-sqr-sqrt
42×add-cube-cbrt
22×fma-def
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 distribute-lft-out-- add-log-exp difference-of-squares
4×expm1-log1p-u cube-mult exp-prod unpow3 log1p-expm1-u sqr-pow
3×flip3-+ exp-diff div-exp frac-add flip-+ associate-/l*
2×log-pow div-inv
1×cbrt-undiv +-commutative pow-to-exp associate-+l- frac-2neg div-sub rem-log-exp pow-exp clear-num sum-log rem-exp-log
Counts
4 → 150
Calls
4 calls:
19.0ms
(/ 0.3333333333333333 (pow N 3))
167.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
188.0ms
(+ (/ (- 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))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 0.3333333333333333 (pow N 3))
41.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
37.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
166.0ms
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

simplify1.2s

Counts
162 → 162
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02212295
14532026
213581829
done50001808

prune564.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch52.0ms

Steps
ItersRangePoint
9
0.00565890190154967
18133.886566758163
4148.853859252382

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02027
12227
done2227

end0.0ms

sample2.9s

Algorithm
intervals
Results
841.0ms8101×body80nan
776.0ms1746×body1280valid
408.0ms1216×body640valid
321.0ms4125×body80valid
103.0ms614×body320valid
33.0ms299×body160valid