Details

Time bar (total: 10.8s)

sample41.0ms

Algorithm
intervals
Results
11.0ms45×body1280valid
7.0ms45×body640valid
6.0ms275×body80nan
6.0ms140×body80valid
1.0ms13×body320valid
1.0ms13×body160valid

simplify3.0ms

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: 27.2b

localize6.0ms

Local error

Found 2 expressions with local error:

2.8b
(log (+ N 1.0))
3.7b
(- (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))

series142.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(log (+ N 1.0))
95.0ms
(- (log (+ N 1.0)) (log N))

simplify2.4s

Counts
47 → 47
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
0101510
1213488
2498445
31321443
44919438
done5000438

prune108.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.6b
(log (/ (+ N 1.0) N))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×div-exp rem-log-exp div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 60
Calls
2 calls:
8.0ms
(/ (+ N 1.0) N)
3.0ms
(log (/ (+ N 1.0) N))

series138.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (+ N 1.0) N)
86.0ms
(log (/ (+ N 1.0) N))

simplify1.1s

Counts
66 → 66
Iterations

Useful iterations: 3 (511.0ms)

IterNodesCost
0108723
1230690
2584637
31748624
done5001624

prune114.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 0.5 (* N N))
0.5b
(/ 0.3333333333333333 (pow N 3))
14.0b
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
35×*-un-lft-identity
34×add-sqr-sqrt
30×add-cube-cbrt
13×add-exp-log associate-/r*
12×unpow-prod-down cube-prod
10×add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×div-exp
4×cube-mult unpow3 sqr-pow
3×pow1 cbrt-undiv frac-sub
2×frac-2neg diff-log clear-num div-inv distribute-lft-out-- difference-of-squares
1×pow-to-exp sub-neg flip3-- flip3-+ frac-add pow-exp prod-exp associate--l+ sum-log flip-- cbrt-unprod flip-+ distribute-lft-out
Counts
3 → 107
Calls
3 calls:
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
321.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series97.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(/ 0.5 (* N N))
36.0ms
(/ 0.3333333333333333 (pow N 3))
35.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify653.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (285.0ms)

IterNodesCost
01971560
14551350
216471282
done50001282

prune204.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

23.2b
(- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N))))))
24.6b
(/ (- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))))) (* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2)))
29.6b
(* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2))
33.6b
(* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
267×associate-*l/
266×associate-*r/
215×frac-add
186×frac-sub
128×frac-times
94×cube-div
71×associate-/l/
55×flip3-+ flip-+
50×flip3-- flip--
36×*-un-lft-identity
24×add-exp-log
23×associate-/r/
17×add-sqr-sqrt
16×associate-*l* add-cbrt-cube
12×unpow-prod-down
11×times-frac
10×add-cube-cbrt
9×pow1 associate-*r* prod-exp distribute-lft-out
8×cube-prod
6×add-log-exp
5×cbrt-unprod unswap-sqr
4×div-exp
3×pow-prod-down associate-/l*
2×cbrt-undiv pow-to-exp pow-exp *-commutative associate--r+ unpow2 sqr-pow
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-sub clear-num associate-/r* sum-cubes div-inv
Counts
4 → 283
Calls
4 calls:
163.0ms
(- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N))))))
468.0ms
(/ (- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))))) (* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2)))
31.0ms
(* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2))
567.0ms
(* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N))

series537.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N))))))
117.0ms
(/ (- (* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N)) (* 0.5 (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))))) (* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2)))
82.0ms
(* (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.3333333333333333 (pow N 3)) (- (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)))) (pow N 2))
274.0ms
(* (+ (pow (/ 1.0 N) 3) (pow (/ 0.3333333333333333 (pow N 3)) 3)) (* N N))

simplify690.0ms

Counts
295 → 295
Iterations

Useful iterations: done (668.0ms)

IterNodesCost
065923677
1224321153
done500120965

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch38.0ms

Steps
ItersRangePoint
10
0.0005333266348582408
117627206.70733242
10132.834563235498

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
12025
done2025

end0.0ms

sample1.2s

Algorithm
intervals
Results
427.0ms1761×body1280valid
183.0ms1221×body640valid
179.0ms7968×body80nan
174.0ms4126×body80valid
57.0ms596×body320valid
18.0ms296×body160valid