Details

Time bar (total: 10.9s)

sample95.0ms

Algorithm
intervals
Results
26.0ms59×body1280valid
23.0ms51×body640valid
14.0ms309×body80nan
10.0ms117×body80valid
4.0ms23×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

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

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:
25.0ms
(- (log (+ N 1.0)) (log N))
11.0ms
(log (+ N 1.0))

series242.0ms

Counts
2 → 6
Calls
2 calls:
146.0ms
(- (log (+ N 1.0)) (log N))
96.0ms
(log (+ N 1.0))

simplify3.1s

Counts
47 → 47
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0101510
1213488
2462445
31063443
42574438
done5001426

prune150.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
59×add-sqr-sqrt
58×*-un-lft-identity
39×add-cube-cbrt
15×associate-/r*
12×unpow-prod-down cube-prod
10×add-exp-log
9×associate-/l*
8×difference-of-squares
7×add-cbrt-cube
5×distribute-lft-out-- add-log-exp
4×cube-mult unpow3 div-exp sqr-pow
3×pow1 distribute-lft-out
2×cbrt-undiv frac-2neg div-sub clear-num div-inv associate-/l/
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ frac-add pow-exp sum-log flip-- flip-+
Counts
3 → 123
Calls
3 calls:
61.0ms
(/ (- 1.0 (/ 0.5 N)) N)
12.0ms
(/ 0.3333333333333333 (pow N 3))
115.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

series176.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- 1.0 (/ 0.5 N)) N)
55.0ms
(/ 0.3333333333333333 (pow N 3))
41.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

simplify1.1s

Counts
132 → 132
Iterations

Useful iterations: 2 (317.0ms)

IterNodesCost
02031721
14381521
211941426
done50001426

prune368.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
56×*-un-lft-identity
41×times-frac
38×cbrt-prod add-cube-cbrt
14×cbrt-div
12×unpow-prod-down cube-prod associate-/r*
11×pow1 add-exp-log swap-sqr
10×difference-of-squares
9×associate-*r* associate-*l*
7×flip3-- pow1/3 flip-- distribute-lft-out--
6×add-cbrt-cube add-log-exp
4×cube-mult frac-times unpow3 unswap-sqr sqr-pow
3×div-exp associate-/l*
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×cbrt-undiv +-commutative pow2 pow-to-exp frac-2neg flip3-+ pow-plus frac-add pow-exp prod-exp clear-num sum-log *-commutative cbrt-unprod flip-+ div-inv distribute-lft-out
Counts
4 → 153
Calls
4 calls:
15.0ms
(cbrt (- 1.0 (/ 0.5 N)))
15.0ms
(/ 0.3333333333333333 (pow N 3))
104.0ms
(* (cbrt (- 1.0 (/ 0.5 N))) (cbrt (- 1.0 (/ 0.5 N))))
215.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (* (cbrt (- 1.0 (/ 0.5 N))) (cbrt (- 1.0 (/ 0.5 N)))) (/ N (cbrt (- 1.0 (/ 0.5 N))))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(cbrt (- 1.0 (/ 0.5 N)))
56.0ms
(/ 0.3333333333333333 (pow N 3))
218.0ms
(* (cbrt (- 1.0 (/ 0.5 N))) (cbrt (- 1.0 (/ 0.5 N))))
51.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (* (cbrt (- 1.0 (/ 0.5 N))) (cbrt (- 1.0 (/ 0.5 N)))) (/ N (cbrt (- 1.0 (/ 0.5 N))))))

simplify1.3s

Counts
165 → 165
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02853006
16192694
219732321
done50002194

prune492.0ms

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))))

rewrite460.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×times-frac
32×add-sqr-sqrt add-cube-cbrt
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 add-log-exp
4×cube-mult exp-prod unpow3 sqr-pow
3×flip3-+ exp-diff div-exp frac-add flip-+ associate-/l* distribute-lft-out--
2×log-pow
1×cbrt-undiv +-commutative pow-to-exp associate-+l- frac-2neg div-sub rem-log-exp pow-exp clear-num sum-log div-inv rem-exp-log
Counts
4 → 120
Calls
4 calls:
17.0ms
(/ 0.3333333333333333 (pow N 3))
114.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
180.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
139.0ms
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 0.3333333333333333 (pow N 3))
63.0ms
(exp (log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))))
52.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
156.0ms
(log (+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3))))

simplify1.1s

Counts
132 → 132
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02132193
14331947
212881740
done50011714

prune756.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

bsearch3.0ms