Details

Time bar (total: 6.0s)

analyze398.0ms (6.6%)

Algorithm
1×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

sample90.0ms (1.5%)

Algorithm
1×intervals
Results
22.0ms256×body80valid
15.0ms27×body1280nan
15.0ms36×body640nan
11.0ms85×body80overflowed
5.0ms7×body160nan
4.0ms15×body320nan
2.0ms29×body80nan
1.0ms9×body80invalid

simplify50.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0498716
1498716

prune7.0ms (0.1%)

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 (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.7%)

Algorithm
1×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:

13.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
11.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms
(* (* 2.0 PI) n)
4.0ms
(/ 1.0 (sqrt k))

series93.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

62.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
20.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
8.0ms
(/ 1.0 (sqrt k))
3.0ms
(* (* 2.0 PI) n)

simplify73.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049532442
149532442

prune409.0ms (6.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1529161
Fresh000
Picked101
Done000
Total1539162

Merged error: 0.0b

Counts
162 → 9

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.6%)

Algorithm
1×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:

13.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
7.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms
(* (* 2.0 PI) n)
5.0ms
(* (* 2.0 PI) n)

series186.0ms (3.1%)

Counts
4 → 12
Calls

4 calls:

152.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
27.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)

simplify41.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050952257

prune341.0ms (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh178
Picked011
Done000
Total1309139

Merged error: 0.0b

Counts
139 → 9

localize16.0ms (0.3%)

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 k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b
(/ 1.0 (sqrt k))

rewrite30.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
48×add-sqr-sqrt
45×add-exp-log
40×times-frac
35×add-cube-cbrt *-un-lft-identity
24×associate-*l*
23×sqrt-prod
22×prod-exp
21×add-cbrt-cube
14×pow1
11×associate-*r*
8×cbrt-unprod
6×div-exp pow-prod-down pow-exp associate-/r* unswap-sqr
4×div-sub add-log-exp sqr-pow
3×*-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-inv pow-sub
1×frac-times unpow-prod-down frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 131
Calls

4 calls:

12.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
5.0ms
(* (* 2.0 PI) n)
5.0ms
(* (* 2.0 PI) n)
4.0ms
(/ 1.0 (sqrt k))

series78.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

63.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
8.0ms
(/ 1.0 (sqrt k))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)

simplify38.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
054762145

prune424.0ms (7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1412143
Fresh167
Picked011
Done011
Total14210152

Merged error: 0b

Counts
152 → 10

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
110×add-exp-log
68×prod-exp
63×add-sqr-sqrt
55×times-frac
50×*-un-lft-identity
44×add-cube-cbrt
27×pow-exp
23×associate-*l* sqrt-prod
20×add-cbrt-cube
19×pow-unpow
18×pow-to-exp
17×div-exp
12×associate-*r*
11×div-sub pow-sub
7×pow1 cbrt-unprod
6×frac-times associate-*l/ associate-/r* unswap-sqr sqr-pow
5×unpow-prod-down
4×associate-*r/ add-log-exp
3×cbrt-undiv div-inv associate-/l* distribute-lft-out-- difference-of-squares
2×pow-pow *-commutative
1×frac-2neg pow-prod-down clear-num
Counts
4 → 180
Calls

4 calls:

14.0ms
(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
10.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
4.0ms
(/ 1.0 (sqrt k))

series152.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

114.0ms
(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
24.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
8.0ms
(/ 1.0 (sqrt k))
5.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify55.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
051533393

prune705.0ms (11.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1902192
Fresh437
Picked011
Done022
Total1948202

Merged error: 0b

Counts
202 → 8

regimes180.0ms (3%)

Accuracy

Total 0.4b remaining (91.1%)

Threshold costs 0.4b (91.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01924
11924

end0.0ms (0%)

sample2.5s (41.4%)

Algorithm
1×intervals
Results
702.0ms8000×body80valid
574.0ms955×body1280nan
370.0ms866×body640nan
336.0ms2439×body80overflowed
124.0ms424×body320nan
41.0ms225×body160nan
41.0ms750×body80nan
25.0ms275×body80invalid

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