Details

Time bar (total: 10.4s)

sample43.0ms

Algorithm
intervals
Results
15.0ms62×body1280valid
6.0ms40×body640valid
5.0ms122×body80valid
5.0ms226×body80nan
2.0ms22×body320valid
1.0ms10×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: 31.3b

localize6.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (log (+ N 1.0)) (log N))
3.9b
(log (+ N 1.0))

rewrite13.0ms

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:
8.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series139.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(- (log (+ N 1.0)) (log N))
45.0ms
(log (+ N 1.0))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: 3 (422.0ms)

IterNodesCost
01271052
1273855
2737705
33047614
done5000614

prune130.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
0.4b
(/ 0.5 (* N N))
0.6b
(/ 0.3333333333333333 (pow N 3))
11.6b
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
843×times-frac
560×prod-diff
554×add-sqr-sqrt
537×*-un-lft-identity
528×add-cube-cbrt
282×associate-+r+
149×unpow-prod-down cube-prod
98×div-inv
51×sqr-pow
50×cube-mult
49×unpow3
40×fma-neg
14×add-exp-log
13×fma-def associate-/r*
11×add-cbrt-cube add-log-exp
10×difference-of-squares
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv frac-add distribute-lft-out--
2×sub-neg flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- distribute-lft-out
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 752
Calls
4 calls:
128.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms
(/ 0.5 (* N N))
7.0ms
(/ 0.3333333333333333 (pow N 3))
53.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
26.0ms
(/ 0.5 (* N N))
35.0ms
(/ 0.3333333333333333 (pow N 3))
88.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify1.5s

Counts
764 → 764
Iterations

Useful iterations: 2 (684.0ms)

IterNodesCost
068424628
1138319119
2387216216
done500016216

prune950.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

11.6b
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
18.0b
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
18.0b
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
18.0b
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
423×times-frac
289×add-sqr-sqrt
282×*-un-lft-identity
280×prod-diff
263×add-cube-cbrt
74×unpow-prod-down cube-prod
48×div-inv
40×fma-neg
26×sqr-pow
25×cube-mult
24×unpow3
15×cbrt-prod cbrt-div
10×difference-of-squares
9×frac-add
6×distribute-lft-out add-log-exp
5×distribute-lft-out--
4×pow1 add-exp-log expm1-log1p-u flip3-- frac-sub add-cbrt-cube flip-- log1p-expm1-u
3×flip3-+ pow1/3 flip-+
1×sub-neg diff-log
Counts
4 → 407
Calls
4 calls:
56.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
87.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
87.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
90.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
157.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
154.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
155.0ms
(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

simplify1.2s

Counts
419 → 419
Iterations

Useful iterations: done (1.2s)

IterNodesCost
048017052
198913388
2352111740
done500011702

prune764.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.0b
(log (/ (+ N 1.0) N))

rewrite13.0ms

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:
8.0ms
(/ (+ N 1.0) N)
3.0ms
(log (/ (+ N 1.0) N))

series132.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ (+ N 1.0) N)
82.0ms
(log (/ (+ N 1.0) N))

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (383.0ms)

IterNodesCost
0112749
1240708
2667660
33011647
done5000647

prune117.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.2b

bsearch34.0ms

Steps
ItersRangePoint
9
0.08347146558812443
2231369.5462890854
9562.64518051556

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01825
12025
done2025

end0.0ms

sample1.2s

Algorithm
intervals
Results
434.0ms1787×body1280valid
191.0ms1261×body640valid
176.0ms7984×body80nan
165.0ms4035×body80valid
61.0ms611×body320valid
18.0ms306×body160valid