Details

Time bar (total: 20.0s)

sample151.0ms

Algorithm
intervals
Results
73.0ms680×body80nan
38.0ms380×body80valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01316
12916
25916
311916
431316
585316
6319616
done500116

prune6.0ms

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))

rewrite172.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 157
Calls
4 calls:
83.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
36.0ms
(* (* 2.0 PI) n)
7.0ms
(/ 1.0 (sqrt k))
40.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series776.0ms

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
43.0ms
(* (* 2.0 PI) n)
48.0ms
(/ 1.0 (sqrt k))
194.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts
169 → 169
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03692880
19612712
231312550
done50002540

prune695.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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))

rewrite162.0ms

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×expm1-log1p-u div-sub log1p-expm1-u 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 → 221
Calls
4 calls:
37.0ms
(* (* 2.0 PI) n)
13.0ms
(/ 1.0 (sqrt k))
58.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
29.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series542.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* 2.0 PI) n)
61.0ms
(/ 1.0 (sqrt k))
215.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
231.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.8s

Counts
233 → 233
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03323588
18543308
224903202
done50023197

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

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))

rewrite119.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 179
Calls
4 calls:
15.0ms
(* n PI)
13.0ms
(/ 1.0 (sqrt k))
34.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
42.0ms
(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series503.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* n PI)
40.0ms
(/ 1.0 (sqrt k))
222.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
218.0ms
(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts
191 → 191
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03982712
110182503
227972409
done50012403

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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))
0.7b
(pow (* n PI) (/ (- 1.0 k) 2.0))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
135×times-frac
103×add-sqr-sqrt
101×*-un-lft-identity
80×pow-unpow
77×add-cube-cbrt
17×add-exp-log
15×pow1
12×sqrt-prod distribute-lft-out-- difference-of-squares
8×add-cbrt-cube
6×associate-/r* div-inv
5×pow-pow pow-prod-down pow-exp prod-exp
4×expm1-log1p-u log1p-expm1-u 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 → 177
Calls
4 calls:
14.0ms
(* n PI)
13.0ms
(/ 1.0 (sqrt k))
64.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
18.0ms
(pow (* n PI) (/ (- 1.0 k) 2.0))

series476.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* n PI)
39.0ms
(/ 1.0 (sqrt k))
234.0ms
(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
167.0ms
(pow (* n PI) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts
189 → 189
Iterations

Useful iterations: done (2.1s)

IterNodesCost
04012593
110232390
228532297
done50002291

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes3.0ms