Details

Time bar (total: 19.3s)

sample138.0ms

Algorithm
intervals
Results
59.0ms680×body80nan
41.0ms380×body80valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01316
12916
25916
311916
431316
584316
6322116
done500116

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 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))
0.6b
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite121.0ms

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:
41.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms
(* (* 2.0 PI) n)
11.0ms
(/ 1.0 (sqrt k))
33.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series794.0ms

Counts
4 → 12
Calls
4 calls:
464.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
49.0ms
(* (* 2.0 PI) n)
75.0ms
(/ 1.0 (sqrt k))
205.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts
161 → 161
Iterations

Useful iterations: 2 (895.0ms)

IterNodesCost
03612800
19312635
230512471
done50012471

prune753.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 PI) n)
0.3b
(/ 1.0 (sqrt k))
0.6b
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
222×times-frac
150×add-sqr-sqrt *-un-lft-identity
122×pow-unpow
114×add-cube-cbrt
23×add-exp-log
21×pow1
18×distribute-lft-out-- difference-of-squares
12×sqrt-prod
11×add-cbrt-cube
9×pow-prod-down prod-exp div-inv
6×pow-pow pow-exp associate-/r*
4×div-sub add-log-exp
3×associate-*r* cbrt-unprod associate-/l*
2×pow-to-exp unpow-prod-down pow-sub sqr-pow
1×cbrt-undiv frac-2neg div-exp associate-*l* clear-num *-commutative
Counts
4 → 213
Calls
4 calls:
28.0ms
(* (* 2.0 PI) n)
6.0ms
(/ 1.0 (sqrt k))
37.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
63.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series505.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* 2.0 PI) n)
65.0ms
(/ 1.0 (sqrt k))
179.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
218.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.9s

Counts
225 → 225
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03263510
18393234
224443128
done50003080

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(* n PI)
0.3b
(/ 1.0 (sqrt k))
0.6b
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b
(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
135×times-frac
103×add-sqr-sqrt
101×*-un-lft-identity
80×pow-unpow
77×add-cube-cbrt
20×add-exp-log
18×pow1
12×sqrt-prod distribute-lft-out-- difference-of-squares
8×add-cbrt-cube
7×pow-prod-down prod-exp
6×pow-pow pow-exp associate-/r* div-inv
4×add-log-exp
3×div-sub associate-*r* associate-*l* associate-/l*
2×pow-to-exp unpow-prod-down pow-sub sqr-pow
1×cbrt-undiv frac-2neg div-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
4 → 171
Calls
4 calls:
11.0ms
(* n PI)
6.0ms
(/ 1.0 (sqrt k))
30.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
36.0ms
(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series534.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* n PI)
52.0ms
(/ 1.0 (sqrt k))
226.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
232.0ms
(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts
183 → 183
Iterations

Useful iterations: 2 (911.0ms)

IterNodesCost
03902642
19972438
227162342
done50022342

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt n)
0.6b
(cbrt n)
0.6b
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b
(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
86×add-sqr-sqrt *-un-lft-identity
80×pow-unpow
62×add-cube-cbrt
29×pow1 add-exp-log
16×pow-prod-down prod-exp
12×distribute-lft-out-- difference-of-squares
9×pow-pow pow-exp
6×cbrt-prod
5×div-inv
4×add-cbrt-cube add-log-exp
3×div-sub
2×pow-to-exp unpow-prod-down pow1/3 pow-sub sqr-pow
Counts
4 → 142
Calls
4 calls:
1.0ms
(cbrt n)
1.0ms
(cbrt n)
49.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
143.0ms
(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

series967.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt n)
241.0ms
(cbrt n)
241.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
238.0ms
(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts
154 → 154
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03172608
18472419
224752180
done50002057

prune985.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes6.0ms