Details

Time bar (total: 2.0s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%0%50%4

sample42.0ms

Algorithm
intervals
Results
19.0ms68×body1280valid
7.0ms36×body640valid
6.0ms115×body80valid
3.0ms24×body320valid
1.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.1b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.8b
(log (+ N 1.0))
4.0b
(- (log (+ N 1.0)) (log N))

rewrite15.0ms

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 → 40
Calls
2 calls:
3.0ms
(log (+ N 1.0))
11.0ms
(- (log (+ N 1.0)) (log N))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(log (+ N 1.0))
6.0ms
(- (log (+ N 1.0)) (log N))

simplify41.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05481434

prune72.0ms

Filtered
35 candidates to 46 candidates (-31.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New44246
Fresh000
Picked101
Done000
Total45247

Merged error: 0.1b

Counts
47 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ 1.0 N) (/ 0.5 (* N N)))
0.1b
(/ 0.5 (* N N))

rewrite14.0ms

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 → 38
Calls
2 calls:
9.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
4.0ms
(/ 0.5 (* N N))

series8.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
3.0ms
(/ 0.5 (* N N))

simplify62.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04863436
14863436

prune51.0ms

Filtered
31 candidates to 44 candidates (-41.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New42244
Fresh011
Picked011
Done000
Total42446

Merged error: 0.1b

Counts
46 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
50×sqrt-prod
33×*-un-lft-identity
27×sqrt-div
26×times-frac
20×pow1 difference-of-squares
17×add-cube-cbrt
16×add-exp-log add-cbrt-cube
15×swap-sqr
11×associate-*r* associate-*l*
9×frac-times flip3-- sqrt-pow1 pow1/2 frac-sub flip--
7×distribute-lft-out--
6×associate-/l*
5×pow-prod-up
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr cbrt-unprod
2×frac-2neg clear-num associate-/r* div-inv
1×pow2 rem-sqrt-square pow-plus sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 144
Calls
4 calls:
9.0ms
(sqrt (- (/ 1.0 N) (/ 0.5 (* N N))))
4.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.5 (* N N))
23.0ms
(* (sqrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (sqrt (- (/ 1.0 N) (/ 0.5 (* N N)))))

series18.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(sqrt (- (/ 1.0 N) (/ 0.5 (* N N))))
3.0ms
(/ 0.5 (* N N))
3.0ms
(/ 0.5 (* N N))
8.0ms
(* (sqrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (sqrt (- (/ 1.0 N) (/ 0.5 (* N N)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
051752198

prune204.0ms

Filtered
94 candidates to 156 candidates (-66.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1560156
Fresh022
Picked011
Done011
Total1564160

Merged error: 0.1b

Counts
160 → 4

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
4.3b
(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×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:
5.0ms
(/ (+ N 1.0) N)
6.0ms
(log (/ (+ N 1.0) N))

series8.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(/ (+ N 1.0) N)
4.0ms
(log (/ (+ N 1.0) N))

simplify40.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
04970619
14970619

prune73.0ms

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

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New64266
Fresh011
Picked011
Done022
Total64670

Merged error: 0.1b

Counts
70 → 6

regimes40.0ms

Accuracy

100% (0.0b remaining)

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

bsearch13.0ms

Steps
ItersRangePoint
9
10428.875531830998
15879139095.133833
292431.2368045783

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03119
13119

end0.0ms

sample1.2s

Algorithm
intervals
Results
514.0ms1780×body1280valid
231.0ms1219×body640valid
205.0ms4068×body80valid
79.0ms630×body320valid
26.0ms303×body160valid

Profiling

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