Details

Time bar (total: 8.7s)

sample216.0ms

Algorithm
intervals
Results
78.0ms970×body80nan
30.0ms355×body80valid
27.0ms46×body1280nan
16.0ms37×body640nan
11.0ms84×body80overflowed
6.0ms21×body320nan
3.0ms12×body160nan

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0499216
1499216

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: 0.3b

Counts
2 → 2

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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:
6.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
9.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms
(* PI n)

series50.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
16.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms
(* PI n)

simplify51.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
049752183
149752183

prune233.0ms

Filtered
82 candidates to 121 candidates (-47.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1129121
Fresh011
Picked101
Done000
Total11310123

Merged error: 0.0b

Counts
123 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
0.2b
(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
0.3b
(* PI (* 2.0 n))
0.3b
(* PI (* 2.0 n))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
358×times-frac
150×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
117×add-exp-log
90×sqrt-prod
71×unpow-prod-down sqr-pow
51×div-exp
39×prod-exp
33×pow-exp
29×associate-/l*
20×pow1
19×add-cbrt-cube
13×pow-unpow
11×pow-to-exp
9×pow-prod-down div-inv
6×associate-*l* associate-/r* cbrt-unprod
4×add-log-exp
3×cbrt-undiv pow-pow
2×associate-*r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 313
Calls
4 calls:
7.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
18.0ms
(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))

series169.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
135.0ms
(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))

simplify91.0ms

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
0497710487
1497710487

prune727.0ms

Filtered
200 candidates to 325 candidates (-62.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3205325
Fresh639
Picked101
Done000
Total3278335

Merged error: 0b

Counts
335 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))))
0.3b
(* PI (* 2.0 n))
0.3b
(* PI (* 2.0 n))
0.3b
(/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
381×add-exp-log
198×prod-exp
142×div-exp
102×pow-exp
34×pow-to-exp
33×times-frac
31×rec-exp 1-exp
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×add-cbrt-cube
18×sqrt-prod
15×pow1
9×associate-/l*
8×cbrt-unprod
7×unpow-prod-down sqr-pow
6×associate-*l* pow-prod-down associate-/r*
5×cbrt-undiv
4×add-log-exp
2×frac-2neg associate-*r* clear-num *-commutative div-inv
1×pow-flip associate-*r/ associate-/r/ inv-pow
Counts
4 → 209
Calls
4 calls:
15.0ms
(/ 1 (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))))
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))
6.0ms
(/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ 1 (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))))
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))
79.0ms
(/ (sqrt k) (pow (* PI (* 2.0 n)) (/ 1.0 2.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
051844547

prune243.0ms

Filtered
82 candidates to 221 candidates (-169.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2210221
Fresh077
Picked011
Done000
Total2218229

Merged error: 0b

Counts
229 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (pow PI (/ k 2.0)))
0.1b
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
0.2b
(/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* 2.0 n) (/ k 2.0))))
0.3b
(* PI (* 2.0 n))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
46×prod-exp
35×times-frac
31×div-exp pow-exp
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
15×pow1 unpow-prod-down
14×pow-to-exp
13×pow-unpow
8×associate-/r* associate-/l*
7×sqr-pow
6×pow-prod-down
4×cbrt-unprod add-log-exp
3×cbrt-undiv rec-exp pow-pow 1-exp associate-*l* div-inv
2×frac-2neg clear-num
1×pow-flip associate-*r* *-commutative inv-pow
Counts
4 → 148
Calls
4 calls:
5.0ms
(/ 1 (pow PI (/ k 2.0)))
6.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
8.0ms
(/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* 2.0 n) (/ k 2.0))))
5.0ms
(* PI (* 2.0 n))

series161.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1 (pow PI (/ k 2.0)))
24.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
126.0ms
(/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* 2.0 n) (/ k 2.0))))
3.0ms
(* PI (* 2.0 n))

simplify51.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049962371
149962371

prune251.0ms

Filtered
86 candidates to 160 candidates (-86.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1600160
Fresh066
Picked011
Done011
Total1608168

Merged error: 0b

Counts
168 → 8

regimes125.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02226
12226

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.1s26966×body80nan
944.0ms10767×body80valid
628.0ms1026×body1280nan
376.0ms836×body640nan
348.0ms2477×body80overflowed
131.0ms425×body320nan
37.0ms214×body160nan

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