Details

Time bar (total: 11.1s)

sample49.0ms

Algorithm
intervals
Results
12.0ms45×body1280valid
10.0ms275×body80nan
8.0ms45×body640valid
7.0ms140×body80valid
2.0ms13×body320valid
1.0ms13×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: 27.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:
2.0ms
(log (+ N 1.0))
8.0ms
(- (log (+ N 1.0)) (log N))

series145.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(log (+ N 1.0))
98.0ms
(- (log (+ N 1.0)) (log N))

simplify3.0s

Counts
71 → 71
Iterations

Useful iterations: 3 (430.0ms)

IterNodesCost
01271052
1279855
2868705
33709614
done5000614

prune154.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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×expm1-log1p-u div-exp rem-log-exp log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 64
Calls
2 calls:
9.0ms
(/ (+ N 1.0) N)
4.0ms
(log (/ (+ N 1.0) N))

series172.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ (+ N 1.0) N)
102.0ms
(log (/ (+ N 1.0) N))

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: 3 (344.0ms)

IterNodesCost
0112749
1240708
2747660
33443647
done5000647

prune141.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
71×times-frac
52×add-sqr-sqrt
48×add-cube-cbrt
35×prod-diff
17×distribute-lft-out
13×add-exp-log associate-/r*
12×unpow-prod-down cube-prod
10×add-cbrt-cube
8×add-log-exp
7×div-inv
6×associate-/l*
5×fma-neg div-exp
4×cube-mult unpow3 sqr-pow
3×pow1 cbrt-undiv expm1-log1p-u frac-sub log1p-expm1-u
2×frac-2neg diff-log clear-num 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-+
Counts
3 → 153
Calls
3 calls:
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
420.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series97.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ 0.5 (* N N))
40.0ms
(/ 0.3333333333333333 (pow N 3))
33.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify1.7s

Counts
162 → 162
Iterations

Useful iterations: 2 (312.0ms)

IterNodesCost
02603457
16242880
231332445
done50012445

prune340.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 0.3333333333333333 (pow N 3))
0.5b
(/ 0.3333333333333333 (pow N 3))
11.8b
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))
11.8b
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt
102×times-frac
68×*-un-lft-identity
56×add-cube-cbrt
28×unpow-prod-down cube-prod
24×associate-/r*
20×hypot-def
14×add-exp-log
12×sqr-pow
10×sqrt-prod
8×cube-mult unpow3 add-cbrt-cube
6×pow1 sqrt-div div-exp associate-/l*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out add-log-exp
2×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 frac-add pow-exp clear-num flip-+ div-inv
Counts
4 → 194
Calls
4 calls:
5.0ms
(/ 0.3333333333333333 (pow N 3))
4.0ms
(/ 0.3333333333333333 (pow N 3))
70.0ms
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))
91.0ms
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 0.3333333333333333 (pow N 3))
37.0ms
(/ 0.3333333333333333 (pow N 3))
47.0ms
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))
45.0ms
(sqrt (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))))

simplify559.0ms

Counts
206 → 206
Iterations

Useful iterations: done (552.0ms)

IterNodesCost
01542240
13261844
212961774
done50001768

prune539.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

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

bsearch35.0ms

Steps
ItersRangePoint
10
0.0005333266348582408
117627206.70733242
10132.834563235498

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
12025
done2025

end0.0ms

sample1.4s

Algorithm
intervals
Results
477.0ms1761×body1280valid
211.0ms1221×body640valid
199.0ms7968×body80nan
193.0ms4126×body80valid
67.0ms596×body320valid
21.0ms296×body160valid