Details

Time bar (total: 6.5s)

analyze382.0ms

Algorithm
search

sample76.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
15.0ms25×body640nan
12.0ms21×body1280nan
9.0ms73×body80overflowed
3.0ms10×body320nan
2.0ms10×body160nan
1.0ms23×body80nan
1.0ms6×body80invalid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0298
1598
21198
33258
410348
550018

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
55×times-frac
49×*-un-lft-identity
46×add-exp-log
43×add-cube-cbrt
23×associate-*l* sqrt-prod
22×prod-exp
19×pow-unpow
16×add-cbrt-cube
15×pow1
9×pow-exp
8×associate-*r*
6×div-exp pow-prod-down associate-/r* unswap-sqr
5×cbrt-unprod sqr-pow
4×add-log-exp
3×pow-to-exp pow-pow div-sub div-inv associate-/l* distribute-lft-out-- pow-sub difference-of-squares
2×cbrt-undiv unpow-prod-down *-commutative
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 149
Calls
4 calls:
12.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms
(* (* 2.0 PI) n)
10.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms
(/ 1.0 (sqrt k))

series87.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms
(* (* 2.0 PI) n)
57.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms
(/ 1.0 (sqrt k))

simplify103.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09531493
142341364
250011350

prune301.0ms

Filtered
107 candidates to 161 candidates (-50.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15011161
Fresh000
Picked101
Done000
Total15111162

Merged error: 0.0b

Counts
162 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
176×add-exp-log
105×prod-exp
39×pow-exp
36×div-exp
26×add-cbrt-cube
20×pow1
13×add-sqr-sqrt pow-to-exp add-cube-cbrt pow-unpow *-un-lft-identity
10×times-frac cbrt-unprod
9×pow-prod-down
6×associate-*r*
4×cbrt-undiv add-log-exp
3×pow-pow
2×associate-*l* *-commutative div-inv
1×unpow-prod-down frac-2neg clear-num associate-/r* associate-/l* sqr-pow
Counts
4 → 118
Calls
4 calls:
6.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
4.0ms
(* (* 2.0 PI) n)
4.0ms
(* (* 2.0 PI) n)
9.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
142.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify99.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
09391410
140821188
250021188

prune191.0ms

Filtered
59 candidates to 130 candidates (-120.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1273130
Fresh3710
Picked011
Done000
Total13011141

Merged error: 0.0b

Counts
141 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) n)
0.2b
(* (* 2.0 PI) n)
0.2b
(/ (* 1.0 (* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.5b
(* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
1023×add-exp-log
763×prod-exp
291×pow-exp
162×div-exp
97×pow-to-exp
37×add-cbrt-cube
16×cbrt-unprod
14×pow1 add-sqr-sqrt
11×associate-*r*
10×add-cube-cbrt *-un-lft-identity
8×sqr-pow
7×associate-*l* pow-prod-down
6×cbrt-undiv
5×swap-sqr
4×unpow-prod-down add-log-exp unswap-sqr
3×*-commutative
1×pow2 frac-2neg times-frac clear-num associate-/r* pow-sqr pow-prod-up div-inv associate-/l*
Counts
4 → 274
Calls
4 calls:
5.0ms
(* (* 2.0 PI) n)
4.0ms
(* (* 2.0 PI) n)
19.0ms
(/ (* 1.0 (* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
8.0ms
(* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
141.0ms
(/ (* 1.0 (* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
107.0ms
(* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)))

simplify143.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
013614341
149023786
250013786

prune241.0ms

Filtered
67 candidates to 286 candidates (-326.9%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2851286
Fresh099
Picked011
Done011
Total28512297

Merged error: 0b

Counts
297 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
162×add-exp-log
97×prod-exp
36×div-exp pow-exp sqrt-prod
28×add-sqr-sqrt
21×pow1
18×add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×pow-to-exp
10×sqrt-pow1 pow1/2 swap-sqr
8×associate-*r* associate-*l*
7×times-frac div-inv
6×sqrt-div
5×pow-prod-up cbrt-unprod
4×cbrt-undiv add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 frac-times frac-2neg pow-plus sqrt-unprod associate-*r/ associate-*l/ clear-num associate-/r* rem-square-sqrt *-commutative associate-/l*
Counts
4 → 143
Calls
4 calls:
11.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms
(sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
6.0ms
(sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
16.0ms
(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
110.0ms
(sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
112.0ms
(sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
140.0ms
(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012853492
150013059

prune462.0ms

Filtered
81 candidates to 155 candidates (-91.4%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1550155
Fresh099
Picked011
Done022
Total15512167

Merged error: 0b

Counts
167 → 12

regimes303.0ms

Accuracy

0% (0.4b 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
01912
11912

end0.0ms

analyze377.0ms

Algorithm
search

sample2.4s

Algorithm
intervals
Results
681.0ms7999×body80valid
591.0ms995×body1280nan
348.0ms812×body640nan
332.0ms2524×body80overflowed
122.0ms406×body320nan
43.0ms731×body80nan
32.0ms194×body160nan
20.0ms224×body80invalid
0.0ms1×body160valid

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