Details

Time bar (total: 22.7s)

sample97.0ms

Algorithm
intervals
Results
23.0ms48×body1280valid
17.0ms54×body640valid
15.0ms286×body80nan
10.0ms122×body80valid
4.0ms20×body320valid
1.0ms12×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize22.0ms

Local error

Found 2 expressions with local error:

2.7b
(- (log (+ N 1.0)) (log N))
2.9b
(log (+ N 1.0))

rewrite57.0ms

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:
45.0ms
(- (log (+ N 1.0)) (log N))
8.0ms
(log (+ N 1.0))

series301.0ms

Counts
2 → 6
Calls
2 calls:
210.0ms
(- (log (+ N 1.0)) (log N))
91.0ms
(log (+ N 1.0))

simplify2.3s

Counts
47 → 47
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0101510
1213488
2643445
32849443
done5001438

prune265.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 N) (/ 0.5 (* N N)))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.4b
(/ 0.5 (* N N))
13.0b
(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
41×add-sqr-sqrt
38×*-un-lft-identity
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 difference-of-squares sqr-pow
3×cbrt-undiv frac-add
2×sub-neg associate-+l+ flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- div-inv distribute-lft-out distribute-lft-out--
1×+-commutative pow-to-exp associate-+l- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 124
Calls
4 calls:
50.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
15.0ms
(/ 0.3333333333333333 (pow N 3))
15.0ms
(/ 0.5 (* N N))
270.0ms
(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
81.0ms
(/ 0.3333333333333333 (pow N 3))
54.0ms
(/ 0.5 (* N N))
69.0ms
(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

simplify4.3s

Counts
136 → 136
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
02101847
15341627
239601528
done50001528

prune654.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (pow (log (+ N 1.0)) 3))
0.4b
(pow (log (+ N 1.0)) 3)
2.7b
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
2.9b
(log (+ N 1.0))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×cbrt-prod
17×*-un-lft-identity
12×add-cube-cbrt
11×pow1
9×unpow-prod-down cube-prod
7×log-prod
6×add-exp-log log-pow
5×add-cbrt-cube add-log-exp difference-of-squares
3×pow-unpow associate--r+ sqr-pow
2×cube-mult log-div unpow3 distribute-lft-out--
1×pow-to-exp sub-neg flip3-- pow-pow flip3-+ pow1/3 diff-log rem-log-exp pow-exp flip-- rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 85
Calls
4 calls:
6.0ms
(cbrt (pow (log (+ N 1.0)) 3))
7.0ms
(pow (log (+ N 1.0)) 3)
71.0ms
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
10.0ms
(log (+ N 1.0))

series542.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(cbrt (pow (log (+ N 1.0)) 3))
184.0ms
(pow (log (+ N 1.0)) 3)
188.0ms
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
88.0ms
(log (+ N 1.0))

simplify2.9s

Counts
97 → 97
Iterations

Useful iterations: 2 (730.0ms)

IterNodesCost
02031422
15561149
225511046
done50021046

prune499.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 0.5 (* N N))
13.0b
(+ (/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N))))) (/ 0.3333333333333333 (pow N 3)))
20.1b
(- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3))
46.5b
(/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N)))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
416×add-sqr-sqrt
262×times-frac
180×difference-of-squares
140×unpow-prod-down cube-prod
117×*-un-lft-identity
60×sqr-pow
56×add-cube-cbrt
48×associate-/l*
28×frac-add
26×distribute-lft-out--
23×associate-/r/
16×frac-times associate-*r/
11×add-exp-log add-cbrt-cube
10×associate-*l/
8×flip3-+ flip-+ add-log-exp
5×difference-cubes
4×pow1 cube-div associate-/r*
3×cbrt-undiv div-exp associate-/l/ distribute-lft-out
2×flip3-- frac-2neg div-sub clear-num frac-sub flip-- div-inv
1×+-commutative associate-+l- sub-neg diff-log prod-exp sum-log cbrt-unprod
Counts
4 → 314
Calls
4 calls:
15.0ms
(/ 0.5 (* N N))
1.3s
(+ (/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N))))) (/ 0.3333333333333333 (pow N 3)))
142.0ms
(- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3))
408.0ms
(/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N)))))

series919.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 0.5 (* N N))
151.0ms
(+ (/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N))))) (/ 0.3333333333333333 (pow N 3)))
253.0ms
(- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3))
472.0ms
(/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N)))))

simplify986.0ms

Counts
326 → 326
Iterations

Useful iterations: done (943.0ms)

IterNodesCost
044917394
1129516838
done500016578

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.3b

bsearch72.0ms

Steps
ItersRangePoint
9
0.5323112742081106
59347805.45921656
4627.670043607516

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12329
done2329

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.7s1813×body1280valid
519.0ms1221×body640valid
479.0ms7916×body80nan
453.0ms4039×body80valid
137.0ms611×body320valid
44.0ms316×body160valid