Details

Time bar (total: 40.7s)

analyze2.7s

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

sample864.0ms

Algorithm
intervals
Results
264.0ms256×body80valid
170.0ms26×body640nan
128.0ms75×body80overflowed
120.0ms32×body1280nan
28.0ms10×body320nan
13.0ms4×body160nan
2.0ms17×body80nan
1.0ms6×body80invalid

simplify575.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (519.0ms)

IterNodesCost
0498825
1498825

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.7b

Counts
2 → 1

localize116.0ms

Local error

Found 4 expressions with local error:

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

rewrite469.0ms

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:
182.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
65.0ms
(* (* 2.0 PI) n)
62.0ms
(/ 1.0 (sqrt k))
97.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series677.0ms

Counts
4 → 12
Calls
4 calls:
383.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
34.0ms
(* (* 2.0 PI) n)
80.0ms
(/ 1.0 (sqrt k))
174.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify721.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (431.0ms)

IterNodesCost
049903938
149903938

prune3.4s

Filtered
109 candidates to 161 candidates (-47.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14813161
Fresh000
Picked101
Done000
Total14913162

Merged error: 0.0b

Counts
162 → 13

localize128.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow n (/ (- 1.0 k) 2.0))
0.3b
(/ 1.0 (sqrt k))
0.3b
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.6b
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
48×times-frac
41×add-cube-cbrt
38×pow-unpow
30×add-exp-log
16×prod-exp
13×pow-exp
12×sqrt-prod
10×unpow-prod-down
9×pow-to-exp sqr-pow
8×pow1 add-cbrt-cube
7×associate-*r*
6×div-sub associate-/r* distribute-lft-out-- pow-sub difference-of-squares unswap-sqr
5×associate-*l*
4×add-log-exp
3×pow-pow div-inv associate-/l*
2×pow-prod-down
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp associate-*l/ clear-num *-commutative cbrt-unprod
Counts
4 → 150
Calls
4 calls:
25.0ms
(pow n (/ (- 1.0 k) 2.0))
17.0ms
(/ 1.0 (sqrt k))
32.0ms
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
77.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series481.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow n (/ (- 1.0 k) 2.0))
42.0ms
(/ 1.0 (sqrt k))
383.0ms
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
23.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify363.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (139.0ms)

IterNodesCost
051423524

prune2.3s

Filtered
111 candidates to 162 candidates (-45.9%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1593162
Fresh3912
Picked011
Done000
Total16213175

Merged error: 0.0b

Counts
175 → 13

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow n (/ (- 1.0 k) 2.0))
0.3b
(/ 1.0 (sqrt k))
0.3b
(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.6b
(pow PI (/ (- 1.0 k) 2.0))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
57×prod-exp
53×add-sqr-sqrt *-un-lft-identity
48×times-frac
41×add-cube-cbrt
38×pow-unpow
30×pow-to-exp pow-exp
14×div-sub pow-sub
12×sqrt-prod
11×add-cbrt-cube
9×unpow-prod-down
7×associate-*r*
6×pow1 associate-/r* distribute-lft-out-- difference-of-squares
5×frac-times associate-*l/
4×add-log-exp
3×associate-*r/ cbrt-unprod div-inv associate-/l* sqr-pow
2×pow-pow pow-prod-down
1×cbrt-undiv frac-2neg div-exp associate-*l* clear-num *-commutative
Counts
4 → 163
Calls
4 calls:
29.0ms
(pow n (/ (- 1.0 k) 2.0))
17.0ms
(/ 1.0 (sqrt k))
45.0ms
(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
22.0ms
(pow PI (/ (- 1.0 k) 2.0))

series353.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow n (/ (- 1.0 k) 2.0))
15.0ms
(/ 1.0 (sqrt k))
265.0ms
(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
9.0ms
(pow PI (/ (- 1.0 k) 2.0))

simplify522.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 0 (298.0ms)

IterNodesCost
051223886

prune2.8s

Filtered
108 candidates to 175 candidates (-62.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1732175
Fresh2911
Picked101
Done011
Total17612188

Merged error: 0b

Counts
188 → 12

localize183.0ms

Local error

Found 4 expressions with local error:

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

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
1069×add-exp-log
906×prod-exp
495×pow-to-exp pow-exp
311×div-exp
32×add-cbrt-cube
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
28×times-frac
13×pow-unpow
12×sqrt-prod cbrt-unprod
7×cbrt-undiv associate-*l* associate-/r*
6×unpow-prod-down
5×pow1
4×associate-*r/ associate-/l* add-log-exp
3×div-inv
2×frac-2neg div-sub clear-num pow-sub sqr-pow
1×pow-pow associate-*r* *-commutative associate-/l/
Counts
4 → 445
Calls
4 calls:
121.0ms
(/ (* (pow n (/ 1.0 2.0)) (* (pow PI (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (pow PI (/ k 2.0)) (pow n (/ k 2.0))))
33.0ms
(/ 1.0 (sqrt k))
73.0ms
(* (pow n (/ 1.0 2.0)) (* (pow PI (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))))
25.0ms
(pow PI (/ 1.0 2.0))

series1.9s

Counts
4 → 10
Calls
4 calls:
1.1s
(/ (* (pow n (/ 1.0 2.0)) (* (pow PI (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (pow PI (/ k 2.0)) (pow n (/ k 2.0))))
64.0ms
(/ 1.0 (sqrt k))
718.0ms
(* (pow n (/ 1.0 2.0)) (* (pow PI (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))))
0.0ms
(pow PI (/ 1.0 2.0))

simplify1.2s

Algorithm
egg-herbie
Counts
455 → 455
Iterations

Useful iterations: 0 (404.0ms)

IterNodesCost
0557318379

prune2.3s

Filtered
88 candidates to 455 candidates (-417.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New4550455
Fresh01010
Picked011
Done011
Total45512467

Merged error: 0b

Counts
467 → 12

regimes1.8s

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify44.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (11.0ms)

IterNodesCost
02834
12834

end0.0ms

sample15.8s

Algorithm
intervals
Results
4.2s8000×body80valid
3.7s992×body1280nan
2.4s2495×body80overflowed
2.3s822×body640nan
835.0ms440×body320nan
277.0ms191×body160nan
251.0ms721×body80nan
116.0ms220×body80invalid

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