Details

Time bar (total: 6.6s)

analyze400.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14

sample102.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0498716
1498716

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
0.3b
(* PI n)
0.3b
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
41×add-sqr-sqrt
39×*-un-lft-identity
33×add-cube-cbrt
23×add-exp-log
19×pow-unpow
18×sqrt-prod
11×pow1
8×unpow-prod-down sqr-pow
7×prod-exp add-cbrt-cube
6×pow-exp associate-/r*
5×div-exp associate-/l*
4×pow-prod-down
3×pow-pow associate-*r* associate-*l* distribute-lft-out-- add-log-exp difference-of-squares
2×pow-to-exp div-sub div-inv pow-sub
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
3 → 112
Calls
3 calls:
7.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
3.0ms
(* PI n)
9.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

series54.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms
(* PI n)
17.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050082183

prune245.0ms

Filtered
80 candidates to 121 candidates (-51.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11011121
Fresh101
Picked101
Done000
Total11211123

Merged error: 0.0b

Counts
123 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
0.3b
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
0.3b
(* PI n)
0.3b
(* PI n)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
358×times-frac
156×add-sqr-sqrt
152×add-cube-cbrt *-un-lft-identity
111×add-exp-log
90×sqrt-prod
71×unpow-prod-down sqr-pow
51×div-exp
35×prod-exp
33×pow-exp
29×associate-/l*
14×pow1
13×pow-unpow add-cbrt-cube
11×pow-to-exp
9×div-inv
6×associate-*r* associate-*l* associate-/r*
5×pow-prod-down
4×add-log-exp
3×cbrt-undiv pow-pow
2×*-commutative cbrt-unprod unswap-sqr
1×frac-2neg clear-num associate-/l/
Counts
4 → 313
Calls
4 calls:
7.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
15.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
3.0ms
(* PI n)
3.0ms
(* PI n)

series155.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
126.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
2.0ms
(* PI n)
2.0ms
(* PI n)

simplify118.0ms

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0498810397
1498810397

prune956.0ms

Filtered
206 candidates to 325 candidates (-57.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3196325
Fresh9110
Picked011
Done000
Total3288336

Merged error: 0b

Counts
336 → 8

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))
0.3b
(* PI n)
0.3b
(* PI (* 2.0 n))
0.3b
(* (pow 2.0 (/ 1.0 2.0)) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
368×add-exp-log
231×prod-exp
121×pow-exp
96×div-exp
65×pow-to-exp
25×add-cbrt-cube
20×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
11×pow1
10×times-frac
9×cbrt-unprod
7×unpow-prod-down
5×associate-/l* sqr-pow
4×cbrt-undiv pow-prod-down add-log-exp unswap-sqr
3×*-commutative
2×div-inv
1×frac-2neg associate-*r/ clear-num associate-/r*
Counts
4 → 189
Calls
4 calls:
10.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))
3.0ms
(* PI n)
5.0ms
(* PI (* 2.0 n))
13.0ms
(* (pow 2.0 (/ 1.0 2.0)) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0)))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))
2.0ms
(* PI n)
3.0ms
(* PI (* 2.0 n))
135.0ms
(* (pow 2.0 (/ 1.0 2.0)) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050074541

prune287.0ms

Filtered
80 candidates to 201 candidates (-151.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2010201
Fresh066
Picked011
Done011
Total2018209

Merged error: 0b

Counts
209 → 8

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (* PI n) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt (sqrt k))))
0.3b
(* PI n)
0.3b
(* PI (* 2.0 n))
0.5b
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt (sqrt k)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
72×sqrt-prod
68×times-frac
55×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
42×prod-exp
32×unpow-prod-down
27×div-exp
25×pow-exp
18×add-cbrt-cube
12×associate-/l* sqr-pow
11×pow1 pow-to-exp
10×associate-/r*
6×associate-*l*
5×cbrt-unprod
4×associate-*r* pow-prod-down add-log-exp
3×cbrt-undiv
2×frac-2neg clear-num *-commutative div-inv
1×unswap-sqr
Counts
4 → 176
Calls
4 calls:
9.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt (sqrt k))))
3.0ms
(* PI n)
5.0ms
(* PI (* 2.0 n))
7.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt (sqrt k)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt (sqrt k))))
2.0ms
(* PI n)
3.0ms
(* PI (* 2.0 n))
48.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt (sqrt k)))

simplify61.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049813152
149813152

prune509.0ms

Filtered
101 candidates to 188 candidates (-86.1%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1880188
Fresh055
Picked011
Done022
Total1888196

Merged error: 0b

Counts
196 → 8

regimes134.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
11824

end0.0ms

sample2.7s

Algorithm
intervals
Results
621.0ms8000×body80valid

Profiling

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