Details

Time bar (total: 4.8s)

sample95.0ms

Algorithm
intervals
Results
34.0ms69×body1280valid
14.0ms276×body80nan
11.0ms35×body640valid
10.0ms121×body80valid
5.0ms25×body320valid
1.0ms6×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0717
1717

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.6b

Counts
2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (log (+ N 1.0)) (log N))
2.5b
(log (+ N 1.0))

rewrite22.0ms

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:
14.0ms
(- (log (+ N 1.0)) (log N))
6.0ms
(log (+ N 1.0))

series16.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(- (log (+ N 1.0)) (log N))
6.0ms
(log (+ N 1.0))

simplify89.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
05481437

prune154.0ms

Filtered
35 candidates to 47 candidates (-34.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New45247
Fresh000
Picked101
Done000
Total46248

Merged error: 0.0b

Counts
48 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ 1.0 N) (/ 0.5 (* N N)))
0.3b
(/ 0.5 (* N N))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
7×add-exp-log times-frac add-cbrt-cube
6×*-un-lft-identity
4×add-cube-cbrt add-log-exp difference-of-squares
3×associate-/l*
2×pow1 cbrt-undiv div-exp
1×sub-neg flip3-- frac-2neg diff-log prod-exp clear-num associate-/r* frac-sub flip-- cbrt-unprod div-inv distribute-lft-out--
Counts
2 → 39
Calls
2 calls:
18.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
8.0ms
(/ 0.5 (* N N))

series16.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
5.0ms
(/ 0.5 (* N N))

simplify107.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
04863442
14863442

prune97.0ms

Filtered
31 candidates to 45 candidates (-45.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New44145
Fresh011
Picked011
Done000
Total44347

Merged error: 0b

Counts
47 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 N))
0.3b
(* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N)))
0.4b
(/ (sqrt 0.5) N)
0.4b
(/ (sqrt 0.5) N)

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
55×times-frac
47×*-un-lft-identity
46×sqrt-prod
43×add-cube-cbrt
13×associate-*r*
12×associate-/l*
10×add-exp-log add-cbrt-cube
9×frac-times sqrt-div difference-of-squares
7×pow1
6×associate-/r*
4×flip3-- flip3-+ associate-*l* frac-add frac-sub flip-- flip-+ add-log-exp
3×associate-*r/ associate-*l/ div-inv
2×cbrt-undiv distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in div-exp clear-num
1×sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 151
Calls
4 calls:
5.0ms
(sqrt (/ 1.0 N))
79.0ms
(* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N)))
10.0ms
(/ (sqrt 0.5) N)
7.0ms
(/ (sqrt 0.5) N)

series62.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(sqrt (/ 1.0 N))
38.0ms
(* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N)))
8.0ms
(/ (sqrt 0.5) N)
8.0ms
(/ (sqrt 0.5) N)

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
050052070

prune655.0ms

Filtered
116 candidates to 163 candidates (-40.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1630163
Fresh011
Picked011
Done011
Total1633166

Merged error: 0b

Counts
166 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
1.9b
(log (/ (+ N 1.0) N))

rewrite20.0ms

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:
9.0ms
(/ (+ N 1.0) N)
8.0ms
(log (/ (+ N 1.0) N))

series19.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(/ (+ N 1.0) N)
6.0ms
(log (/ (+ N 1.0) N))

simplify74.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
04970619
14970619

prune152.0ms

Filtered
48 candidates to 66 candidates (-37.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New66066
Fresh000
Picked011
Done022
Total66369

Merged error: 0b

Counts
69 → 3

regimes53.0ms

Accuracy

100% (0.0b remaining)

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

bsearch29.0ms

Steps
ItersRangePoint
10
0.01683730658649282
149997866560.9553
174026.59391661748

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03119
13119

end0.0ms

sample2.9s

Algorithm
intervals
Results
958.0ms1747×body1280valid
462.0ms8017×body80nan
458.0ms1266×body640valid
369.0ms4071×body80valid
151.0ms621×body320valid
43.0ms295×body160valid

Profiling

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