Details

Time bar (total: 10.3s)

sample43.0ms

Algorithm
intervals
Results
13.0ms56×body1280valid
8.0ms52×body640valid
6.0ms276×body80nan
5.0ms127×body80valid
1.0ms12×body320valid
1.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(log (+ N 1.0))
2.8b
(- (log (+ N 1.0)) (log N))

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:
2.0ms
(log (+ N 1.0))
6.0ms
(- (log (+ N 1.0)) (log N))

series328.0ms

Counts
2 → 6
Calls
2 calls:
233.0ms
(log (+ N 1.0))
94.0ms
(- (log (+ N 1.0)) (log N))

simplify2.7s

Counts
47 → 47
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
0101510
1213488
2498445
31320443
44438438
done5001438

prune112.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (+ N 1.0))
2.6b
(log (+ N 1.0))
2.6b
(log (+ N 1.0))
2.7b
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×log-prod
21×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
8×associate--l+
7×pow1 add-exp-log distribute-rgt-in distribute-lft-in
6×log-div associate--r+ add-log-exp
5×distribute-lft-out
4×add-cbrt-cube
3×flip3-+ rem-log-exp log-pow flip-+
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
2.0ms
(log (+ N 1.0))
3.0ms
(log (+ N 1.0))
2.0ms
(log (+ N 1.0))
8.0ms
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(log (+ N 1.0))
44.0ms
(log (+ N 1.0))
41.0ms
(log (+ N 1.0))
140.0ms
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

simplify1.5s

Counts
84 → 84
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01551223
13631157
210941025
33778998
done5001997

prune229.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.3b
(/ 0.5 (* N N))
10.8b
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity times-frac
35×add-sqr-sqrt
31×add-cube-cbrt
14×add-exp-log
13×associate-/r*
12×unpow-prod-down cube-prod
11×add-cbrt-cube add-log-exp
6×associate-/l*
5×div-exp
4×pow1 cube-mult unpow3 sqr-pow
3×cbrt-undiv frac-sub distribute-lft-out
2×frac-2neg flip3-+ diff-log frac-add clear-num sum-log flip-+ div-inv distribute-lft-out-- difference-of-squares
1×+-commutative pow-to-exp sub-neg flip3-- pow-exp prod-exp associate--l+ flip-- cbrt-unprod
Counts
4 → 121
Calls
4 calls:
30.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
4.0ms
(/ 0.3333333333333333 (pow N 3))
3.0ms
(/ 0.5 (* N N))
296.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
40.0ms
(/ 0.3333333333333333 (pow N 3))
26.0ms
(/ 0.5 (* N N))
32.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify844.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (319.0ms)

IterNodesCost
02011812
14641577
216701491
done50001491

prune236.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)))
0.1b
(/ (/ 0.5 N) N)
0.2b
(/ 0.3333333333333333 (pow N 3))
10.8b
(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
125×add-sqr-sqrt
88×*-un-lft-identity
71×add-cube-cbrt
16×associate-/l*
15×unpow-prod-down cube-prod associate-/r* difference-of-squares
14×add-exp-log
11×add-cbrt-cube add-log-exp
7×sqr-pow
6×div-exp div-inv
4×pow1 cbrt-undiv cube-mult unpow3 distribute-lft-out--
3×frac-add distribute-lft-out
2×sub-neg associate-+r+ flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip--
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp flip-+ associate-/l/
Counts
4 → 186
Calls
4 calls:
235.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)))
6.0ms
(/ (/ 0.5 N) N)
4.0ms
(/ 0.3333333333333333 (pow N 3))
85.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

series186.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)))
24.0ms
(/ (/ 0.5 N) N)
38.0ms
(/ 0.3333333333333333 (pow N 3))
90.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

simplify1.2s

Counts
198 → 198
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03162966
17292669
219762482
done50012478

prune384.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch27.0ms

Steps
ItersRangePoint
7
1766.3470775505596
94269.73169533648
3632.967761108044

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02338
12638
done2638

end0.0ms

sample1.3s

Algorithm
intervals
Results
429.0ms1744×body1280valid
189.0ms1269×body640valid
188.0ms8134×body80nan
165.0ms4056×body80valid
60.0ms613×body320valid
19.0ms318×body160valid