Details

Time bar (total: 10.0m)

sample218.0ms

Algorithm
intervals
Results
119.0ms655×body80nan
67.0ms365×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
62053
5821
4322
3123
260
129
013

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.3b
(* PI (* n 2))
1.4b
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
493×times-frac
383×add-sqr-sqrt
380×*-un-lft-identity
378×add-cube-cbrt
328×unpow-prod-up
312×prod-diff
141×sqrt-prod
46×associate-/l*
26×add-exp-log
25×div-inv
14×pow1
10×add-cbrt-cube
9×prod-exp
8×sub-neg unpow-prod-down sqr-pow
6×pow-unpow associate-/r* pow-prod-down pow-exp
5×div-exp
3×expm1-log1p-u pow-pow associate-*l* cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-sub difference-of-squares
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative distribute-lft-out-- associate-/l/
Counts
3 → 436
Calls
3 calls:
35.0ms
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
21.0ms
(* PI (* n 2))
16.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series564.0ms

Counts
3 → 9
Calls
3 calls:
334.0ms
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
36.0ms
(* PI (* n 2))
193.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.7s

Counts
445 → 445
Iterations
IterNodes
24287
11515
0698

prune7.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
0.2b
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
0.5b
(pow PI (- 1/2 (/ k 2)))
1.3b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
43085×times-frac
25423×add-sqr-sqrt
25417×*-un-lft-identity
25413×add-cube-cbrt
23985×unpow-prod-up
22815×prod-diff
6903×sqrt-prod
1806×div-inv
1151×unpow-prod-down
585×sub-neg sqr-pow
327×associate-/r*
54×associate-/l*
53×add-exp-log pow-sub
51×associate-/r/
31×div-exp
16×pow-exp
12×pow-unpow
11×pow-to-exp add-cbrt-cube
8×pow1
5×prod-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×pow-pow
2×clear-num frac-2neg distribute-lft-out--
1×pow-prod-down associate-/l/
Counts
4 → 14326
Calls
4 calls:
53.0ms
(/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
14.0ms
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
6.0ms
(pow PI (- 1/2 (/ k 2)))
10.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series973.0ms

Counts
4 → 12
Calls
4 calls:
530.0ms
(/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
217.0ms
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
78.0ms
(pow PI (- 1/2 (/ k 2)))
148.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.1m

Counts
14338 → 14338
Iterations
IterNodes
139008
013501

prune4.4m

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))
0.2b
(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
0.2b
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
1.3b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite3.5s

Algorithm
rewrite-expression-head
Rules
95305×times-frac
57519×add-sqr-sqrt
57506×*-un-lft-identity
57500×add-cube-cbrt
55651×unpow-prod-up
53454×prod-diff
51126×sqrt-prod
3833×div-inv
3787×unpow-prod-down
1240×sqr-pow
957×sub-neg
327×associate-/r*
116×associate-/l*
115×pow-sub
113×associate-/r/
77×add-exp-log
49×div-exp
38×pow-exp
19×pow-to-exp
17×pow-unpow
11×add-cbrt-cube
8×difference-of-squares
7×pow1 prod-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×pow-pow distribute-lft-out--
2×clear-num frac-2neg
1×pow-prod-down associate-/l/
Counts
4 → 31889
Calls
4 calls:
11.0ms
(pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))
82.0ms
(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
9.0ms
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
9.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series6.1s

Counts
4 → 12
Calls
4 calls:
1.3s
(pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))
4.5s
(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
146.0ms
(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
87.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify3.1m

Iterations
IterNodes
023788