Details

Time bar (total: 12.1s)

sample54.0ms

Algorithm
intervals
Results
16.0ms55×body1280valid
8.0ms46×body640valid
8.0ms252×body80nan
6.0ms125×body80valid
2.0ms17×body320valid
1.0ms13×body160valid

simplify15.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize8.0ms

Local error

Found 2 expressions with local error:

3.2b
(- (log (+ N 1.0)) (log N))
4.1b
(log (+ N 1.0))

rewrite54.0ms

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:
46.0ms
(- (log (+ N 1.0)) (log N))
5.0ms
(log (+ N 1.0))

series164.0ms

Counts
2 → 6
Calls
2 calls:
117.0ms
(- (log (+ N 1.0)) (log N))
48.0ms
(log (+ N 1.0))

simplify958.0ms

Counts
47 → 47

prune164.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))) (* 1.0 (/ 1 N)))
0.1b
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
0.3b
(/ 1 (pow N 2))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
67×times-frac
46×*-un-lft-identity
36×add-cube-cbrt
32×add-exp-log
28×associate-*l*
23×unpow-prod-down
16×associate-*r/
14×frac-add
12×div-exp
11×associate-*r*
10×prod-exp add-cbrt-cube
9×frac-times unpow2 unswap-sqr sqr-pow
8×associate-/r*
7×un-div-inv
6×pow-to-exp rec-exp flip3-- 1-exp pow-exp frac-sub flip-- difference-of-squares
5×pow1 add-log-exp
4×distribute-rgt-in sub-neg associate-+l+ distribute-lft-in
3×associate-*l/ associate-/l*
2×cbrt-undiv cbrt-unprod div-inv distribute-lft-out--
1×+-commutative pow-flip frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ inv-pow
Counts
3 → 166
Calls
3 calls:
93.0ms
(+ (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))) (* 1.0 (/ 1 N)))
281.0ms
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
29.0ms
(/ 1 (pow N 2))

series174.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))) (* 1.0 (/ 1 N)))
110.0ms
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
24.0ms
(/ 1 (pow N 2))

simplify1.6s

Counts
175 → 175

prune492.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.3b
(log (/ (+ N 1.0) N))

rewrite54.0ms

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:
38.0ms
(/ (+ N 1.0) N)
12.0ms
(log (/ (+ N 1.0) N))

series188.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(/ (+ N 1.0) N)
126.0ms
(log (/ (+ N 1.0) N))

simplify1.2s

Counts
66 → 66

prune171.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))))) (* 1.0 (/ 1 N)))
0.1b
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
0.3b
(/ 1 (pow N 2))
2.0b
(log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
67×times-frac
49×*-un-lft-identity
39×add-cube-cbrt
33×add-exp-log
28×associate-*l*
23×unpow-prod-down
14×log-prod
12×div-exp
11×associate-*r* add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×exp-sum associate-/r*
7×pow1 associate-+l+
6×distribute-rgt-in pow-to-exp sub-neg rec-exp distribute-lft-in 1-exp pow-exp add-log-exp difference-of-squares
3×frac-times associate-*r/ log-pow associate-/l*
2×cbrt-undiv flip3-- frac-sub flip-- cbrt-unprod div-inv distribute-lft-out--
1×+-commutative exp-prod exp-to-pow pow-flip frac-2neg flip3-+ rem-log-exp pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-+ inv-pow
Counts
4 → 173
Calls
4 calls:
52.0ms
(+ (log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))))) (* 1.0 (/ 1 N)))
259.0ms
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
9.0ms
(/ 1 (pow N 2))
40.0ms
(log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0))))) (* 1.0 (/ 1 N)))
132.0ms
(* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))
33.0ms
(/ 1 (pow N 2))
147.0ms
(log (exp (* (/ 1 (pow N 2)) (- (/ (/ 6004799503160661.0 18014398509481984.0) N) (/ 1.0 2.0)))))

simplify1.5s

Counts
185 → 185

prune620.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.0b

bsearch33.0ms

Steps
ItersRangePoint
6
9556.682540875734
100426.34546533476
9772.093561518632

simplify779.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
790.0ms1714×body1280valid
460.0ms8150×body80nan
410.0ms1276×body640valid
368.0ms4126×body80valid
107.0ms591×body320valid
32.0ms293×body160valid