Details

Time bar (total: 9.0s)

sample190.0ms

Algorithm
intervals
Results
73.0ms886×body80nan
29.0ms338×body80valid
21.0ms34×body1280nan
12.0ms84×body80overflowed
8.0ms19×body640nan
4.0ms15×body320nan
1.0ms7×body160nan

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0298
1598
21198
33258
410348
550018

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

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))

rewrite34.0ms

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:
9.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms
(* (* 2.0 PI) n)
11.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms
(/ 1.0 (sqrt k))

series89.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms
(* (* 2.0 PI) n)
62.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms
(/ 1.0 (sqrt k))

simplify105.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09531493
142341364
250011350

prune312.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15110161
Fresh000
Picked101
Done000
Total15210162

Merged error: 0.0b

Counts
162 → 10

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))))

rewrite34.0ms

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:
7.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms
(* (* 2.0 PI) n)
5.0ms
(* (* 2.0 PI) n)
10.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
145.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify101.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
09391410
140821188
250021188

prune209.0ms

Filtered
60 candidates to 130 candidates (-116.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1264130
Fresh459
Picked011
Done000
Total13010140

Merged error: 0.0b

Counts
140 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

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))))
0.2b
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.4b
(* (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))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
323×add-exp-log
196×prod-exp
72×div-exp pow-exp
35×add-cbrt-cube
26×sqrt-prod
25×add-sqr-sqrt
24×pow1 pow-to-exp
13×add-cube-cbrt *-un-lft-identity
12×cbrt-unprod
11×associate-*r*
10×swap-sqr
9×associate-*l*
8×cbrt-undiv sqrt-pow1 pow1/2
6×times-frac pow-prod-down div-inv
5×pow-prod-up
4×sqrt-div add-log-exp unswap-sqr
3×pow-sqr
2×frac-2neg clear-num associate-/r* *-commutative associate-/l*
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ rem-square-sqrt
Counts
4 → 182
Calls
4 calls:
5.0ms
(* (* 2.0 PI) n)
10.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
10.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
17.0ms
(* (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))))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* 2.0 PI) n)
146.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
144.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
150.0ms
(* (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))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011493651
150013072

prune415.0ms

Filtered
74 candidates to 194 candidates (-162.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1931194
Fresh358
Picked011
Done011
Total1968204

Merged error: 0.0b

Counts
204 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
49×prod-exp
37×add-cbrt-cube
34×sqrt-prod
30×add-sqr-sqrt
21×pow1
18×div-exp
16×cbrt-unprod
14×add-cube-cbrt *-un-lft-identity associate-*r*
10×swap-sqr associate-*l* sqr-pow
9×pow-prod-down pow-exp unswap-sqr
6×cbrt-undiv sqrt-pow1 pow1/2
4×unpow-prod-down add-log-exp
3×pow-to-exp pow-sqr *-commutative pow-prod-up
1×pow2 frac-2neg times-frac pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt div-inv associate-/l*
Counts
4 → 131
Calls
4 calls:
5.0ms
(* (* 2.0 PI) n)
5.0ms
(* (* 2.0 PI) n)
18.0ms
(/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
10.0ms
(* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
146.0ms
(/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
109.0ms
(* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))

simplify128.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
09141861
146411418
250011398

prune252.0ms

Filtered
73 candidates to 143 candidates (-95.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1421143
Fresh055
Picked011
Done112
Total1438151

Merged error: 0.0b

Counts
151 → 8

regimes243.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02822
12822

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.2s27279×body80nan
907.0ms10629×body80valid
632.0ms1022×body1280nan
353.0ms2462×body80overflowed
338.0ms747×body640nan
139.0ms460×body320nan
39.0ms224×body160nan

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