Details

Time bar (total: 6.6s)

analyze392.0ms

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

sample91.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
20.0ms34×body1280nan
13.0ms31×body640nan
11.0ms78×body80overflowed
6.0ms22×body320nan
1.0ms21×body80nan
1.0ms3×body160nan
0.0ms5×body80invalid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

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: 0.3b

Counts
2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

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

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

series54.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms
(* PI n)
36.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))

simplify47.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050082183

prune227.0ms

Filtered
80 candidates to 121 candidates (-51.3%)
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 (* 2.0 (* PI n)) (/ 1.0 2.0))
0.2b
(* PI n)
0.2b
(* PI n)
0.2b
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))

rewrite44.0ms

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:
6.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
4.0ms
(* PI n)
3.0ms
(* PI n)
15.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))

series162.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
2.0ms
(* PI n)
2.0ms
(* PI n)
133.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))

simplify109.0ms

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0498810397
1498810397

prune724.0ms

Filtered
204 candidates to 325 candidates (-59.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3241325
Fresh189
Picked011
Done000
Total32510335

Merged error: 0b

Counts
335 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
146×add-sqr-sqrt
144×*-un-lft-identity
138×add-cube-cbrt
78×sqrt-prod
69×add-exp-log
40×associate-/r*
32×unpow-prod-down div-exp sqr-pow
19×pow-unpow
16×prod-exp
15×pow-exp
13×pow1 add-cbrt-cube
9×associate-/l*
7×div-inv
6×rec-exp 1-exp div-sub associate-/r/ pow-sub
5×pow-to-exp
4×cbrt-undiv pow-prod-down add-log-exp
3×pow-pow associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num
1×pow-flip *-commutative cbrt-unprod inv-pow unswap-sqr
Counts
4 → 288
Calls
4 calls:
11.0ms
(/ 1 (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))))
9.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms
(* PI n)
6.0ms
(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))

series139.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))))
16.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms
(* PI n)
67.0ms
(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))

simplify78.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
055577167

prune478.0ms

Filtered
164 candidates to 300 candidates (-82.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3000300
Fresh088
Picked011
Done011
Total30010310

Merged error: 0b

Counts
310 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
118×add-exp-log
81×times-frac
73×add-sqr-sqrt
66×associate-*l*
56×sqrt-prod
51×prod-exp
46×add-cube-cbrt *-un-lft-identity
43×div-exp
37×unpow-prod-down
34×add-cbrt-cube
24×sqr-pow
18×associate-*r*
16×pow-exp
12×unswap-sqr
11×pow-to-exp cbrt-unprod
10×pow1
9×cbrt-undiv
8×associate-/l*
4×add-log-exp
3×pow-prod-down *-commutative div-inv
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num associate-/r*
Counts
4 → 194
Calls
4 calls:
4.0ms
(* PI n)
3.0ms
(* PI n)
27.0ms
(* (/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (pow 2.0 (/ k 2.0))) (/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* PI n) (/ k 2.0)))))
9.0ms
(/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* PI n) (/ k 2.0))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI n)
2.0ms
(* PI n)
167.0ms
(* (/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (pow 2.0 (/ k 2.0))) (/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* PI n) (/ k 2.0)))))
128.0ms
(/ (sqrt (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* PI n) (/ k 2.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050476318

prune656.0ms

Filtered
136 candidates to 206 candidates (-51.5%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2060206
Fresh077
Picked011
Done022
Total20610216

Merged error: 0b

Counts
216 → 10

regimes267.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
11824

end0.0ms

sample2.5s

Algorithm
intervals
Results
692.0ms8000×body80valid
590.0ms982×body1280nan
366.0ms823×body640nan
343.0ms2419×body80overflowed
137.0ms440×body320nan
43.0ms725×body80nan
40.0ms230×body160nan
21.0ms235×body80invalid

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