Details

Time bar (total: 8.9s)

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))

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:
6.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series144.0ms

Counts
2 → 6
Calls
2 calls:
96.0ms
(- (log (+ N 1.0)) (log N))
47.0ms
(log (+ N 1.0))

simplify2.3s

Counts
47 → 47
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
0101510
1213488
2499445
31320443
44897438
done5000438

prune111.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity times-frac
35×add-sqr-sqrt
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 sqr-pow
3×cbrt-undiv frac-sub distribute-lft-out
2×frac-2neg flip3-+ diff-log frac-add clear-num sum-log flip-+ div-inv distribute-lft-out-- difference-of-squares
1×+-commutative pow-to-exp sub-neg flip3-- pow-exp prod-exp associate--l+ flip-- cbrt-unprod
Counts
4 → 121
Calls
4 calls:
34.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
327.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series188.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
26.0ms
(/ 0.5 (* N N))
38.0ms
(/ 0.3333333333333333 (pow N 3))
35.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify800.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (312.0ms)

IterNodesCost
02011812
14641577
216691491
done50001491

prune247.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

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)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
54×times-frac
40×*-un-lft-identity
31×add-cube-cbrt
14×add-exp-log unpow-prod-down cube-prod
13×associate-/r*
11×add-cbrt-cube add-log-exp
10×difference-of-squares
6×associate-/l* sqr-pow
5×cube-mult div-exp
4×pow1 unpow3
3×cbrt-undiv frac-add distribute-lft-out--
2×sub-neg associate-+r+ flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- div-inv distribute-lft-out
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 131
Calls
4 calls:
104.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
40.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
27.0ms
(/ 0.5 (* N N))
43.0ms
(/ 0.3333333333333333 (pow N 3))
97.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify815.0ms

Counts
143 → 143
Iterations

Useful iterations: 2 (360.0ms)

IterNodesCost
02152088
15071835
216531733
done50011733

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))

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)
4.0ms
(log (/ (+ N 1.0) N))

series147.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(/ (+ N 1.0) N)
92.0ms
(log (/ (+ N 1.0) N))

simplify1.4s

Counts
66 → 66
Iterations

Useful iterations: 3 (367.0ms)

IterNodesCost
0108723
1230690
2584637
31748624
done5000624

prune253.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

100% (0.0b remaining)

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

bsearch37.0ms

Steps
ItersRangePoint
9
0.08347146558812443
2231369.5462890854
9562.64518051556

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
12025
done2025

end0.0ms

sample1.3s

Algorithm
intervals
Results
440.0ms1787×body1280valid
191.0ms1261×body640valid
186.0ms7984×body80nan
166.0ms4035×body80valid
60.0ms611×body320valid
19.0ms306×body160valid