Migdal et al, Equation (51)

Time bar (total: 11.8s)

analyze128.0ms (1.1%)

Memory
-0.1MiB live, 159.8MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.4s (28.7%)

Memory
-52.8MiB live, 5 533.4MiB allocated
Samples
1.4s5 453×1invalid
1.2s8 256×0valid
155.0ms457×2invalid
32.0ms395×0invalid
26.0ms229×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-pow: 685.0ms (32.2% of total)
ival-mult: 469.0ms (22% of total)
ival-div: 378.0ms (17.8% of total)
ival-sqrt: 173.0ms (8.1% of total)
ival-sub: 155.0ms (7.3% of total)
ival-pi: 121.0ms (5.7% of total)
adjust: 114.0ms (5.4% of total)
...in/eval/compile.rkt:110:19: 15.0ms (0.7% of total)
ival-true: 12.0ms (0.6% of total)
ival-assert: 6.0ms (0.3% of total)
Bogosity

preprocess53.0ms (0.4%)

Memory
-3.5MiB live, 47.7MiB allocated
Algorithm
2×egg-herbie
Rules
260×associate-*r*
160×sub-neg
158×associate-*l*
138×distribute-lft-neg-in
124×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033104
18788
220288
339488
462188
589088
6105988
7126488
8132388
9134788
10136588
11136988
12136988
01316
12814
24514
36614
48414
59914
612014
714714
815614
915914
015913
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
Call 2
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ (pow (* (* 2 (PI)) n) (+ 1/2 (* k -1/2))) (sqrt k))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(/ (pow (* (* 2 (PI)) n) (- 1/2 (* k -1/2))) (sqrt (neg k)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(/ (pow (* n (* (PI) -2)) (+ 1/2 (* k -1/2))) (sqrt k))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(/ (pow (* (* 2 (PI)) n) (- 1/2 (* k -1/2))) (neg (sqrt (neg k))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(/ (pow (* n (* (PI) -2)) (+ 1/2 (* k -1/2))) (neg (sqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(/ (pow (* (PI) (* k 2)) (- 1/2 (* n 1/2))) (sqrt n))

explain153.0ms (1.3%)

Memory
-13.5MiB live, 339.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
490(2.3125173411975517e-132 3.8023544145460047e+186)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-k
00-0-n
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-(sqrt.f64 k)
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity9419
Confusion
Predicted +Predicted -
+40
-90162
Precision
0.0425531914893617
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+400
-9019143
Precision?
0.035398230088495575
Recall?
1.0
Freqs
test
numberfreq
0162
194
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
59.0ms512×0valid
Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-pow: 10.0ms (26.2% of total)
ival-mult: 9.0ms (23.6% of total)
ival-div: 8.0ms (21% of total)
ival-sqrt: 6.0ms (15.7% of total)
ival-sub: 3.0ms (7.9% of total)
ival-pi: 2.0ms (5.2% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify9.0ms (0.1%)

Memory
19.5MiB live, 19.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Rules
64×*-lowering-*.f32
64×*-lowering-*.f64
48×+-lowering-+.f64
48×+-lowering-+.f32
36×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
12852
24552
36652
48452
59952
612052
714752
815652
915952
015949
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/ 1 (sqrt k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
1
#s(literal 1 binary64)
(sqrt k)
(sqrt.f64 k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* (* 2 (PI)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(* 2 (PI))
(*.f64 #s(literal 2 binary64) (PI.f64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
n
(/ (- 1 k) 2)
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(- 1 k)
(-.f64 #s(literal 1 binary64) k)

localize44.0ms (0.4%)

Memory
10.5MiB live, 88.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.7%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Samples
28.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-pow: 6.0ms (31.6% of total)
ival-div: 4.0ms (21.1% of total)
ival-mult: 4.0ms (21.1% of total)
ival-sqrt: 2.0ms (10.5% of total)
ival-pi: 1.0ms (5.3% of total)
ival-sub: 1.0ms (5.3% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series92.0ms (0.8%)

Memory
-30.9MiB live, 171.7MiB allocated
Counts
5 → 84
Calls
Call 1
Inputs
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (* (* 2 (PI)) n)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
Calls

21 calls:

TimeVariablePointExpression
43.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
31.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite293.0ms (2.5%)

Memory
43.5MiB live, 549.1MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 378×*-lowering-*.f32
4 378×*-lowering-*.f64
3 286×pow-lowering-pow.f64
3 286×pow-lowering-pow.f32
2 442×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01338
18035
248833
3445133
0857233
Stop Event
1×iter limit
1×node limit
Counts
5 → 253
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
(sqrt k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
Outputs
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
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(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 0 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 #s(literal 1 binary64) k))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (neg.f64 (/.f64 (*.f64 k (*.f64 k k)) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 #s(literal 1 binary64) k)))))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (neg.f64 (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 0 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (PI.f64))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) n))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (PI.f64))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 (PI.f64) n))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 n)))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 n)) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 n (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (*.f64 n #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify403.0ms (3.4%)

Memory
-9.2MiB live, 826.5MiB allocated
Algorithm
1×egg-herbie
Rules
11 382×accelerator-lowering-fma.f32
11 382×accelerator-lowering-fma.f64
6 430×*-lowering-*.f32
6 430×*-lowering-*.f64
2 486×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01201122
13211103
29541013
33225986
45231908
08739896
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) #s(literal 1/8 binary64)))) (*.f64 k k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (+.f64 (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 k (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))

eval40.0ms (0.3%)

Memory
-10.8MiB live, 106.3MiB allocated
Compiler

Compiled 7 188 to 889 computations (87.6% saved)

prune45.0ms (0.4%)

Memory
8.1MiB live, 129.7MiB allocated
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New32215337
Fresh000
Picked101
Done000
Total32315338
Accuracy
100.0%
Counts
338 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.3%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
99.3%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
99.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
▶46.2%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
45.7%
(*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 2 binary64)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
77.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
▶46.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
▶32.6%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶99.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.2%
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶42.3%
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
Compiler

Compiled 556 to 406 computations (27% saved)

simplify249.0ms (2.1%)

Memory
24.3MiB live, 421.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓cost-diff0
(/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
✓cost-diff128
(-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓cost-diff6592
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff64
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff64
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
✓cost-diff0
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff128
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
✓cost-diff0
(*.f64 n (PI.f64))
✓cost-diff0
(/.f64 (*.f64 n (PI.f64)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff64
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff64
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Rules
3 340×accelerator-lowering-fma.f32
3 340×accelerator-lowering-fma.f64
2 970×*-lowering-*.f32
2 970×*-lowering-*.f64
2 636×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039267
179265
2138261
3260258
4418258
5678251
61189251
71930251
82752248
93526248
104848248
116887248
08185242
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(sqrt (/ 1 k))
(/ 1 k)
1
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 2)
2
(/ 1 (/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))))
1
(/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))
(sqrt k)
k
(pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(+ 1/2 (/ k 2))
1/2
(/ k 2)
(* (/ 1 (sqrt k)) (* (sqrt 2) (sqrt (* n (PI)))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(* (sqrt 2) (sqrt (* n (PI))))
(sqrt 2)
2
(sqrt (* n (PI)))
(* n (PI))
n
(PI)
(exp (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k))))
(- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))
(/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k)))
(log (* (PI) (* 2 n)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(/ 2 (+ 1 k))
(+ 1 k)
1
k
(* 1/2 (log k))
1/2
(log k)
Outputs
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(sqrt (/ 1 k))
(pow.f64 k #s(literal -1/2 binary64))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* (* 2 (PI)) n)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(* 2 (PI))
(*.f64 #s(literal 2 binary64) (PI.f64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
n
(/ (- 1 k) 2)
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(- 1 k)
(-.f64 #s(literal 1 binary64) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(* n (PI))
(*.f64 (PI.f64) n)
n
(PI)
(PI.f64)
k
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1 (/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1 binary64) k)) k))
1
#s(literal 1 binary64)
(/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1 binary64) k))))
(sqrt k)
(sqrt.f64 k)
k
(pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* (PI) (* 2 n))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
n
(+ 1/2 (/ k 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ k 2)
(/.f64 k #s(literal 2 binary64))
(* (/ 1 (sqrt k)) (* (sqrt 2) (sqrt (* n (PI)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/ 1 (sqrt k))
(pow.f64 k #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(sqrt k)
(sqrt.f64 k)
k
(* (sqrt 2) (sqrt (* n (PI))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 (PI.f64) n))
(* n (PI))
(*.f64 (PI.f64) n)
n
(PI)
(PI.f64)
(exp (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1 binary64) k)) k))
(- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (+.f64 #s(literal 1 binary64) k)) (log.f64 k)))
(/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k)))
(/.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
(log (* (PI) (* 2 n)))
(log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
(* (PI) (* 2 n))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
n
(/ 2 (+ 1 k))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))
(+ 1 k)
(+.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(* 1/2 (log k))
(*.f64 #s(literal 1/2 binary64) (log.f64 k))
1/2
#s(literal 1/2 binary64)
(log k)
(log.f64 k)

localize208.0ms (1.8%)

Memory
-29.2MiB live, 329.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy99.6%
(-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓accuracy96.1%
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓accuracy49.3%
(PI.f64)
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
✓accuracy99.7%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓accuracy49.3%
(PI.f64)
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
✓accuracy99.7%
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
✓accuracy99.7%
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy49.3%
(PI.f64)
✓accuracy99.9%
(*.f64 n (PI.f64))
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy85.6%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓accuracy49.3%
(PI.f64)
✓accuracy99.9%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.7%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy49.3%
(PI.f64)
Samples
62.0ms133×0exit
44.0ms122×0valid
0.0ms1×0invalid
Compiler

Compiled 271 to 41 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 81.0ms
ival-div: 33.0ms (40.9% of total)
ival-mult: 14.0ms (17.3% of total)
ival-pow: 11.0ms (13.6% of total)
ival-sqrt: 8.0ms (9.9% of total)
ival-log: 6.0ms (7.4% of total)
ival-add: 3.0ms (3.7% of total)
ival-exp: 2.0ms (2.5% of total)
ival-sub: 2.0ms (2.5% of total)
ival-pi: 1.0ms (1.2% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series76.0ms (0.6%)

Memory
31.5MiB live, 150.5MiB allocated
Counts
22 → 396
Calls
Call 1
Inputs
#<alt (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (sqrt (/ 1 k))>
#<alt (/ 1 k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (/ 1 (/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))))>
#<alt (/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))>
#<alt (sqrt k)>
#<alt (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))>
#<alt (* (/ 1 (sqrt k)) (* (sqrt 2) (sqrt (* n (PI)))))>
#<alt (/ 1 (sqrt k))>
#<alt (* (sqrt 2) (sqrt (* n (PI))))>
#<alt (exp (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k))))>
#<alt (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))>
#<alt (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k)))>
#<alt (log (* (PI) (* 2 n)))>
#<alt (PI)>
#<alt (* (* 2 (PI)) n)>
#<alt (* (PI) (* 2 n))>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
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#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
Calls

99 calls:

TimeVariablePointExpression
24.0ms
k
@0
(- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))
16.0ms
n
@0
(exp (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k))))
3.0ms
k
@inf
(/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))
2.0ms
k
@-inf
(- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))
1.0ms
k
@0
(/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))

rewrite433.0ms (3.7%)

Memory
-30.7MiB live, 728.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 044×*-lowering-*.f32
5 044×*-lowering-*.f64
3 768×/-lowering-/.f32
3 768×/-lowering-/.f64
2 840×pow-lowering-pow.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039179
1227167
21603164
08474162
Stop Event
1×iter limit
1×node limit
Counts
22 → 1 074
Calls
Call 1
Inputs
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(sqrt (/ 1 k))
(/ 1 k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(/ 1 (/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))))
(/ (sqrt k) (pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2))))
(sqrt k)
(pow (* (PI) (* 2 n)) (+ 1/2 (/ k 2)))
(* (/ 1 (sqrt k)) (* (sqrt 2) (sqrt (* n (PI)))))
(/ 1 (sqrt k))
(* (sqrt 2) (sqrt (* n (PI))))
(exp (- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k))))
(- (/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k))) (* 1/2 (log k)))
(/ (log (* (PI) (* 2 n))) (/ 2 (+ 1 k)))
(log (* (PI) (* 2 n)))
(PI)
(* (* 2 (PI)) n)
(* (PI) (* 2 n))
Outputs
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)))
(fabs.f64 (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) k))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) #s(literal -1 binary64))
(pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) k)))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)))
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))
(neg.f64 (/.f64 #s(literal -1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) k)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) k))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) k))))
(pow.f64 k #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) k)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) k))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)))
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(*.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 k k) #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 k (*.f64 k k)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 k k))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (-.f64 #s(literal 1 binary64) (*.f64 k k)))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) (*.f64 k (*.f64 k k))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) (*.f64 k (-.f64 k #s(literal 1 binary64))))))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
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(+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (log.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(+.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64))) (log.f64 (PI.f64)))
(+.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))
(+.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(-.f64 (/.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (/.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)) (log.f64 (/.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(fma.f64 #s(literal 1 binary64) (log.f64 (PI.f64)) (log.f64 (*.f64 #s(literal 2 binary64) n)))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) (log.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 (*.f64 #s(literal 2 binary64) n)))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (log.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(fma.f64 (log.f64 (PI.f64)) #s(literal 1 binary64) (log.f64 (*.f64 #s(literal 2 binary64) n)))
(fma.f64 #s(literal 3 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) (log.f64 (*.f64 #s(literal 2 binary64) n)))
(fma.f64 #s(literal 1/3 binary64) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 #s(literal 2 binary64) n)))
(/.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 #s(literal 2 binary64) n))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64))) (log.f64 (/.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 #s(literal 2 binary64) n)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(/.f64 (+.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 3 binary64)) (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) (log.f64 (PI.f64))))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) n))))))
(/.f64 (+.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 n) (log.f64 n)) (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(/.f64 (+.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (log.f64 n) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 (log.f64 n) (log.f64 n)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) n))) (PI.f64))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) n))) (PI.f64))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))

simplify500.0ms (4.2%)

Memory
-3.0MiB live, 760.3MiB allocated
Algorithm
1×egg-herbie
Rules
11 826×accelerator-lowering-fma.f32
11 826×accelerator-lowering-fma.f64
6 370×*-lowering-*.f32
6 370×*-lowering-*.f64
3 778×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03085141
19884921
233634637
080874580
Stop Event
1×iter limit
1×node limit
Counts
396 → 396
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
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(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(* 1/2 (* k (log (* 2 (* n (PI))))))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(* 1/2 (* k (log (* 2 (* n (PI))))))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(+ (log n) (log (* 2 (PI))))
(+ (log n) (log (* 2 (PI))))
(+ (log n) (log (* 2 (PI))))
(+ (log n) (log (* 2 (PI))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 k (*.f64 k k)) (PI.f64)) n))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 k (*.f64 k k)) (PI.f64)) n)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 k (*.f64 k k)) (PI.f64)) n)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))))))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+.f64 (*.f64 k (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) k))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))) (*.f64 k k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(* -1 (* k (+ (* -1 (/ (- (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (+ (log -1) (* -1 (log (/ -1 k)))))) k)) (* -1/2 (log (* 2 (* n (PI))))))))
(*.f64 (-.f64 #s(literal 0 binary64) k) (-.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/2 binary64) k) (+.f64 (-.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) k))))))
(* 1/2 (* (+ 1 k) (+ (log n) (log (* 2 (PI))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log n) (log (* 2 (PI))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log n) (log (* 2 (PI))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log n) (log (* 2 (PI))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (* (+ 1 k) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (+.f64 k #s(literal 1 binary64))))
(* 1/2 (log (* 2 (* n (PI)))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (log (* 2 (* n (PI)))))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* 1/2 (* k (log (* 2 (* n (PI))))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(* 1/2 (* k (log (* 2 (* n (PI))))))
(*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(* -1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* -1/2 (/ (log (* 2 (* n (PI)))) k)))))
(*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
(+ (log n) (log (* 2 (PI))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log n) (log (* 2 (PI))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log n) (log (* 2 (PI))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log n) (log (* 2 (PI))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))

eval224.0ms (1.9%)

Memory
23.2MiB live, 497.8MiB allocated
Compiler

Compiled 35 132 to 4 140 computations (88.2% saved)

prune386.0ms (3.3%)

Memory
-8.8MiB live, 307.1MiB allocated
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New1 692181 710
Fresh7310
Picked415
Done000
Total1 703221 725
Accuracy
100.0%
Counts
1 725 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
85.3%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
▶99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
99.3%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
46.9%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
99.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
▶33.7%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
33.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
46.9%
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
46.9%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
46.9%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
46.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓32.6%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶99.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
▶32.5%
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
32.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
46.9%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
96.2%
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶32.7%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
32.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
95.1%
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
30.6%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 627 to 487 computations (22.3% saved)

simplify16.0ms (0.1%)

Memory
11.8MiB live, 11.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
✓cost-diff0
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)
✓cost-diff0
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
✓cost-diff0
(/.f64 k (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Rules
184×*-lowering-*.f32
184×*-lowering-*.f64
96×associate-*r*
72×associate-*l*
60×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030191
152191
290191
3130191
4192191
5259191
6281191
7314191
8356191
9364191
10365191
0365188
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(sqrt k)
(sqrt (/ (* 2 (* (PI) n)) k))
(/ (* 2 (* (PI) n)) k)
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
k
(/ (sqrt 2) (sqrt (/ k (* (PI) n))))
(sqrt 2)
2
(sqrt (/ k (* (PI) n)))
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
(* (sqrt (* (* (/ 1 k) 2) n)) (sqrt (PI)))
(sqrt (* (* (/ 1 k) 2) n))
(* (* (/ 1 k) 2) n)
(* (/ 1 k) 2)
(/ 1 k)
1
k
2
n
(sqrt (PI))
(PI)
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
(sqrt (/ 1 k))
(/ 1 k)
1
k
(pow (sqrt (* 2 (* (PI) n))) (- 1 k))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1 k)
Outputs
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* 2 (* (PI) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1/2 (/ k 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ k 2)
(/.f64 k #s(literal 2 binary64))
k
(sqrt k)
(sqrt.f64 k)
(sqrt (/ (* 2 (* (PI) n)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(/ (* 2 (* (PI) n)) k)
(/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(* 2 (* (PI) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
k
(/ (sqrt 2) (sqrt (/ k (* (PI) n))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (/ k (* (PI) n)))
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(/ k (* (PI) n))
(/.f64 k (*.f64 (PI.f64) n))
k
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(* (sqrt (* (* (/ 1 k) 2) n)) (sqrt (PI)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64)))
(sqrt (* (* (/ 1 k) 2) n))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k))
(* (* (/ 1 k) 2) n)
(/.f64 (*.f64 #s(literal 2 binary64) n) k)
(* (/ 1 k) 2)
(/.f64 #s(literal 2 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
2
#s(literal 2 binary64)
n
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 1 binary64) k)))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(pow (sqrt (* 2 (* (PI) n))) (- 1 k))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 1 binary64) k))
(sqrt (* 2 (* (PI) n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(* 2 (* (PI) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1 k)
(-.f64 #s(literal 1 binary64) k)

localize186.0ms (1.6%)

Memory
24.5MiB live, 179.6MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy99.6%
(PI.f64)
✓accuracy99.4%
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
✓accuracy98.4%
(sqrt.f64 (PI.f64))
✓accuracy73.0%
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy99.3%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
✓accuracy73.0%
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
✓accuracy99.7%
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy73.0%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
✓accuracy99.8%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.7%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
Samples
100.0ms255×0valid
0.0ms1×0invalid
Compiler

Compiled 201 to 32 computations (84.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 54.0ms
ival-mult: 19.0ms (34.9% of total)
ival-sqrt: 13.0ms (23.9% of total)
ival-div: 9.0ms (16.5% of total)
ival-pow: 9.0ms (16.5% of total)
ival-sub: 3.0ms (5.5% of total)
ival-pi: 1.0ms (1.8% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series132.0ms (1.1%)

Memory
-23.4MiB live, 91.1MiB allocated
Counts
21 → 360
Calls
Call 1
Inputs
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (sqrt (/ (* 2 (* (PI) n)) k))>
#<alt (/ (* 2 (* (PI) n)) k)>
#<alt (/ (sqrt 2) (sqrt (/ k (* (PI) n))))>
#<alt (sqrt 2)>
#<alt (sqrt (/ k (* (PI) n)))>
#<alt (/ k (* (PI) n))>
#<alt (* (/ 1 k) 2)>
#<alt (* (sqrt (* (* (/ 1 k) 2) n)) (sqrt (PI)))>
#<alt (sqrt (* (* (/ 1 k) 2) n))>
#<alt (* (* (/ 1 k) 2) n)>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))>
#<alt (sqrt (/ 1 k))>
#<alt (/ 1 k)>
#<alt (pow (sqrt (* 2 (* (PI) n))) (- 1 k))>
#<alt (PI)>
#<alt (sqrt (PI))>
#<alt (sqrt (* 2 (* (PI) n)))>
Outputs
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* (sqrt (/ n k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
Calls

90 calls:

TimeVariablePointExpression
46.0ms
n
@0
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
35.0ms
n
@-inf
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
21.0ms
n
@0
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
7.0ms
n
@inf
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
1.0ms
n
@-inf
(/ (sqrt 2) (sqrt (/ k (* (PI) n))))

rewrite450.0ms (3.8%)

Memory
16.6MiB live, 379.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 988×*-lowering-*.f32
4 988×*-lowering-*.f64
4 290×/-lowering-/.f32
4 290×/-lowering-/.f64
1 680×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030132
1172127
21123127
08285127
Stop Event
1×iter limit
1×node limit
Counts
21 → 1 129
Calls
Call 1
Inputs
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
(* (PI) n)
(sqrt (/ (* 2 (* (PI) n)) k))
(/ (* 2 (* (PI) n)) k)
(/ (sqrt 2) (sqrt (/ k (* (PI) n))))
(sqrt 2)
(sqrt (/ k (* (PI) n)))
(/ k (* (PI) n))
(* (/ 1 k) 2)
(* (sqrt (* (* (/ 1 k) 2) n)) (sqrt (PI)))
(sqrt (* (* (/ 1 k) 2) n))
(* (* (/ 1 k) 2) n)
(* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
(sqrt (/ 1 k))
(/ 1 k)
(pow (sqrt (* 2 (* (PI) n))) (- 1 k))
(PI)
(sqrt (PI))
(sqrt (* 2 (* (PI) n)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(exp.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) k)))
(exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 k #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (neg.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))))
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(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
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simplify784.0ms (6.6%)

Memory
5.7MiB live, 629.4MiB allocated
Algorithm
1×egg-herbie
Rules
11 960×accelerator-lowering-fma.f32
11 960×accelerator-lowering-fma.f64
5 310×*-lowering-*.f32
5 310×*-lowering-*.f64
3 760×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02083838
15993749
217773552
326963524
449553523
088143465
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
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(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
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(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* (sqrt (/ n k)) (sqrt 2))
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
Outputs
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n)))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n)))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n)))) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
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(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) #s(literal 2 binary64)))) (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))))))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 k k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))

eval244.0ms (2.1%)

Memory
28.3MiB live, 498.9MiB allocated
Compiler

Compiled 30 426 to 3 228 computations (89.4% saved)

prune226.0ms (1.9%)

Memory
-39.8MiB live, 452.0MiB allocated
Pruning

33 alts after pruning (32 fresh and 1 done)

PrunedKeptTotal
New1 797251 822
Fresh9716
Picked415
Done101
Total1 811331 844
Accuracy
100.0%
Counts
1 844 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
32.5%
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
33.7%
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
▶85.3%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
21.3%
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
70.7%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
46.8%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
46.9%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
32.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)))
33.7%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
33.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
33.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
46.9%
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
46.9%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
▶46.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
32.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
70.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))))
▶46.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
32.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
46.9%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
32.5%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
46.9%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶32.6%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
32.6%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
32.6%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
32.6%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
32.7%
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
32.7%
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
32.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
32.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
32.6%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
▶32.6%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
30.6%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 826 to 646 computations (21.8% saved)

simplify17.0ms (0.1%)

Memory
0.7MiB live, 40.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 #s(literal 2 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 #s(literal 2 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓cost-diff128
(/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 #s(literal 2 binary64) k)
✓cost-diff0
(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓cost-diff0
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
✓cost-diff0
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))
✓cost-diff64
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
✓cost-diff128
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k))
Rules
180×*-lowering-*.f32
180×*-lowering-*.f64
116×/-lowering-/.f32
116×/-lowering-/.f64
94×times-frac
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027177
154171
296171
3167171
4270171
5318171
6339171
7372171
8411171
0411171
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
(pow (* 2 (* (PI) n)) (- 1 k))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1 k)
1
k
(/ 1 k)
1/2
(sqrt (* n (* (/ 2 k) (PI))))
(* n (* (/ 2 k) (PI)))
n
(* (/ 2 k) (PI))
(/ 2 k)
2
k
(PI)
(sqrt (/ (/ 2 k) (/ 1 (* (PI) n))))
(/ (/ 2 k) (/ 1 (* (PI) n)))
(/ 2 k)
2
k
(/ 1 (* (PI) n))
1
(* (PI) n)
(PI)
n
(* (sqrt (/ 2 k)) (sqrt (* (PI) n)))
(sqrt (/ 2 k))
(/ 2 k)
2
k
(sqrt (* (PI) n))
(* (PI) n)
(PI)
n
(* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
Outputs
(pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(pow (* 2 (* (PI) n)) (- 1 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1 k)
(-.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1/2
#s(literal 1/2 binary64)
(sqrt (* n (* (/ 2 k) (PI))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(* n (* (/ 2 k) (PI)))
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
n
(* (/ 2 k) (PI))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
(PI)
(PI.f64)
(sqrt (/ (/ 2 k) (/ 1 (* (PI) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(/ (/ 2 k) (/ 1 (* (PI) n)))
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
(/ 1 (* (PI) n))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
1
#s(literal 1 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(* (sqrt (/ 2 k)) (sqrt (* (PI) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt (/ 2 k))
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
(sqrt (* (PI) n))
(sqrt.f64 (*.f64 (PI.f64) n))
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/ 1 (sqrt k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
1
#s(literal 1 binary64)
(sqrt k)
(sqrt.f64 k)
k
(sqrt (* 2 (* (PI) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n

localize105.0ms (0.9%)

Memory
35.2MiB live, 311.0MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) n))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy99.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
✓accuracy99.6%
(PI.f64)
✓accuracy99.6%
(/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
✓accuracy73.0%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓accuracy99.7%
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
✓accuracy99.6%
(PI.f64)
✓accuracy99.5%
(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓accuracy73.0%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓accuracy99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(PI.f64)
✓accuracy85.6%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
Samples
58.0ms255×0valid
0.0ms1×0invalid
Compiler

Compiled 184 to 29 computations (84.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-sqrt: 11.0ms (28.1% of total)
ival-div: 10.0ms (25.5% of total)
ival-mult: 9.0ms (23% of total)
ival-pow: 5.0ms (12.8% of total)
ival-pi: 2.0ms (5.1% of total)
ival-sub: 1.0ms (2.6% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory
-30.5MiB live, 46.3MiB allocated
Counts
20 → 336
Calls
Call 1
Inputs
#<alt (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))>
#<alt (pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)>
#<alt (pow (* 2 (* (PI) n)) (- 1 k))>
#<alt (* 2 (* (PI) n))>
#<alt (sqrt (* n (* (/ 2 k) (PI))))>
#<alt (* n (* (/ 2 k) (PI)))>
#<alt (* (/ 2 k) (PI))>
#<alt (/ 2 k)>
#<alt (/ (/ 2 k) (/ 1 (* (PI) n)))>
#<alt (sqrt (/ (/ 2 k) (/ 1 (* (PI) n))))>
#<alt (/ 1 (* (PI) n))>
#<alt (* (sqrt (/ 2 k)) (sqrt (* (PI) n)))>
#<alt (sqrt (/ 2 k))>
#<alt (sqrt (* (PI) n))>
#<alt (* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (PI)>
#<alt (* (PI) n)>
Outputs
#<alt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)>
#<alt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)>
#<alt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)>
#<alt (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (- (* -1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))) k)>
#<alt (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))>
#<alt (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))>
#<alt (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))>
#<alt (* 2 (* n (PI)))>
#<alt (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))>
#<alt (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1 k)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1 k)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1 k)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1 k)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (/ 1 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
Calls

84 calls:

TimeVariablePointExpression
2.0ms
n
@0
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
1.0ms
k
@0
(pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)
1.0ms
n
@-inf
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
1.0ms
k
@-inf
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
1.0ms
n
@-inf
(pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)

rewrite365.0ms (3.1%)

Memory
5.1MiB live, 719.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 806×*-lowering-*.f32
5 806×*-lowering-*.f64
2 668×/-lowering-/.f32
2 668×/-lowering-/.f64
1 266×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027120
1153119
2962119
08366119
Stop Event
1×iter limit
1×node limit
Counts
20 → 1 420
Calls
Call 1
Inputs
(* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k))
(pow (* (pow (* 2 (* (PI) n)) (- 1 k)) (/ 1 k)) 1/2)
(pow (* 2 (* (PI) n)) (- 1 k))
(* 2 (* (PI) n))
(sqrt (* n (* (/ 2 k) (PI))))
(* n (* (/ 2 k) (PI)))
(* (/ 2 k) (PI))
(/ 2 k)
(/ (/ 2 k) (/ 1 (* (PI) n)))
(sqrt (/ (/ 2 k) (/ 1 (* (PI) n))))
(/ 1 (* (PI) n))
(* (sqrt (/ 2 k)) (sqrt (* (PI) n)))
(sqrt (/ 2 k))
(sqrt (* (PI) n))
(* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))
(/ 1 (sqrt k))
(sqrt k)
(sqrt (* 2 (* (PI) n)))
(PI)
(* (PI) n)
Outputs
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal -1 binary64) k)))
(neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) k)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 0 binary64) k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k))))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 #s(literal 1 binary64) (/.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)) (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 k #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) k)))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 k #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) k))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 0 binary64) k))
(/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))) (*.f64 k (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 #s(literal 2 binary64) k) k))
(/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (*.f64 k (pow.f64 #s(literal 2 binary64) k))) (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 #s(literal 1/2 binary64) k) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 0 binary64) k)) k))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 0 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (*.f64 (PI.f64) n) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) (/.f64 n (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k)))
(*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k))))
(*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) k))
(*.f64 (/.f64 #s(literal 2 binary64) (*.f64 k (pow.f64 #s(literal 2 binary64) k))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 0 binary64) k)))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 0 binary64) k)) #s(literal 1 binary64)))
(*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) k) (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) k) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (pow.f64 #s(literal 2 binary64) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 #s(literal 2 binary64) k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 n k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k) (/.f64 (PI.f64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) k) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) k)) k))
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(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
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(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
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(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))
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(/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
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(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 #s(literal -1 binary64) (PI.f64)))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) #s(literal -1 binary64))
(*.f64 (PI.f64) n)
(*.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) n))
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) n)))
(*.f64 n (PI.f64))
(*.f64 n (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
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(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
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(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))

simplify484.0ms (4.1%)

Memory
14.4MiB live, 987.9MiB allocated
Algorithm
1×egg-herbie
Rules
11 682×accelerator-lowering-fma.f32
11 682×accelerator-lowering-fma.f64
7 598×*-lowering-*.f32
7 598×*-lowering-*.f64
2 138×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01473143
13723113
211442945
338212893
085212877
Stop Event
1×iter limit
1×node limit
Counts
336 → 336
Calls
Call 1
Inputs
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(* 2 (/ (* n (PI)) k))
(/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
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(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (- (* -1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))) k)
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
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(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(* 2 (* n (PI)))
(+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))
(+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))
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(exp (* (log (* 2 (* n (PI)))) (- 1 k)))
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(exp (* (log (* 2 (* n (PI)))) (- 1 k)))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
Outputs
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)
(/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(/.f64 (*.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(literal -2 binary64))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) k)
(/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (*.f64 (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (+.f64 (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal -2 binary64))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) k)
(/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal -2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 k #s(literal -1/3 binary64))))))) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k)))))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (*.f64 k k) (*.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (- (* -1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (*.f64 k k) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (*.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 n #s(literal -1/3 binary64))) (/.f64 n (*.f64 k #s(literal -2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))) k)
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(* 2 (* n (PI)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))
(*.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(literal -2 binary64)))))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))

eval333.0ms (2.8%)

Memory
7.5MiB live, 653.5MiB allocated
Compiler

Compiled 34 477 to 4 671 computations (86.5% saved)

prune334.0ms (2.8%)

Memory
-3.9MiB live, 486.7MiB allocated
Pruning

36 alts after pruning (31 fresh and 5 done)

PrunedKeptTotal
New2 322112 333
Fresh72027
Picked145
Done011
Total2 330362 366
Accuracy
100.0%
Counts
2 366 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
32.5%
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
33.7%
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
✓85.3%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
73.0%
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) #s(literal 1/2 binary64))
21.3%
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
46.8%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
46.9%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
32.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)))
33.7%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
33.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
46.9%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓46.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
32.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
✓46.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
32.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
46.9%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
32.5%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
46.9%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
85.4%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
32.6%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
32.6%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
32.6%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
32.6%
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
32.6%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
32.6%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
32.6%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
32.6%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
32.7%
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
32.7%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
32.6%
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
32.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
32.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
32.6%
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
✓32.6%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
30.6%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 1 306 to 598 computations (54.2% saved)

regimes88.0ms (0.7%)

Memory
-0.4MiB live, 196.8MiB allocated
Counts
70 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

22.0ms
n
21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms
k
19.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes34.0ms (0.3%)

Memory
0.6MiB live, 81.3MiB allocated
Counts
47 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
Calls

2 calls:

15.0ms
k
14.0ms
n
Results
AccuracySegmentsBranch
99.6%2k
85.4%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory
20.7MiB live, 57.7MiB allocated
Counts
43 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) n)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
Outputs
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
Calls

2 calls:

14.0ms
n
12.0ms
k
Results
AccuracySegmentsBranch
46.9%1n
49.5%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory
-13.4MiB live, 25.4MiB allocated
Counts
33 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
Calls

1 calls:

10.0ms
k
Results
AccuracySegmentsBranch
49.5%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory
3.2MiB live, 41.9MiB allocated
Counts
24 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
Outputs
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
Calls

2 calls:

8.0ms
n
7.0ms
k
Results
AccuracySegmentsBranch
33.7%1n
36.3%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory
-4.7MiB live, 36.6MiB allocated
Counts
23 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 n #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n))))
Outputs
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
Calls

2 calls:

9.0ms
n
7.0ms
k
Results
AccuracySegmentsBranch
33.7%1n
33.7%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory
16.4MiB live, 16.4MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
Outputs
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
Calls

2 calls:

4.0ms
n
4.0ms
k
Results
AccuracySegmentsBranch
32.7%1k
32.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Memory
11.7MiB live, 11.7MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1/2 binary64))))
Outputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
Calls

2 calls:

2.0ms
n
2.0ms
k
Results
AccuracySegmentsBranch
32.6%1k
32.6%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Memory
-32.8MiB live, 6.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
Outputs
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
Calls

2 calls:

2.0ms
n
1.0ms
k
Results
AccuracySegmentsBranch
32.6%1k
32.6%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch16.0ms (0.1%)

Memory
20.9MiB live, 20.9MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
1.2832908501053174e-55
1.8939050852348016e-53
Samples
10.0ms112×0valid
Compiler

Compiled 210 to 172 computations (18.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-div: 2.0ms (26.6% of total)
ival-mult: 2.0ms (26.6% of total)
ival-pow: 2.0ms (26.6% of total)
ival-sub: 1.0ms (13.3% of total)
ival-sqrt: 1.0ms (13.3% of total)
ival-pi: 0.0ms (0% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

bsearch24.0ms (0.2%)

Memory
-18.6MiB live, 20.6MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.2518002864851643e+192
1.3288009965493239e+194
Samples
18.0ms112×0valid
Compiler

Compiled 245 to 165 computations (32.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-div: 2.0ms (28.6% of total)
ival-mult: 2.0ms (28.6% of total)
ival-pow: 2.0ms (28.6% of total)
ival-sub: 1.0ms (14.3% of total)
ival-sqrt: 1.0ms (14.3% of total)
ival-pi: 0.0ms (0% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

bsearch16.0ms (0.1%)

Memory
20.6MiB live, 20.6MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
1.2518002864851643e+192
1.3288009965493239e+194
Samples
10.0ms112×0valid
Compiler

Compiled 245 to 165 computations (32.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 2.0ms (28.4% of total)
ival-pow: 2.0ms (28.4% of total)
ival-div: 1.0ms (14.2% of total)
ival-sub: 1.0ms (14.2% of total)
ival-sqrt: 1.0ms (14.2% of total)
ival-pi: 0.0ms (0% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

bsearch43.0ms (0.4%)

Memory
-3.6MiB live, 35.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
41.0ms
1.2950777552430778e+178
2.261392898037942e+181
Samples
37.0ms128×0valid
Compiler

Compiled 277 to 186 computations (32.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-pi: 26.0ms (77.5% of total)
ival-div: 2.0ms (6% of total)
ival-mult: 2.0ms (6% of total)
ival-pow: 2.0ms (6% of total)
ival-sub: 1.0ms (3% of total)
ival-sqrt: 1.0ms (3% of total)
...in/eval/compile.rkt:110:19: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

simplify14.0ms (0.1%)

Memory
-32.7MiB live, 20.4MiB allocated
Algorithm
1×egg-herbie
Rules
26×*-commutative_binary64
10×+-commutative_binary64
10×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058162
175162
285162
391162
495162
596162
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7548785066802179/431359146674410236714672241392314090778194310760649159697657763987456 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 18500000000000001326515528856118709499189173587193619563203030027870830436603239197790903729406958111819908389287495204814218322087696297758769814497440667877670401432246318046823106924035178496 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 1800000000000000098948217486616420690110293681291206783925489232159862801485652853510527459077704553512813339997251871140538313039388899041893541449142923046752364560243159124418911144144535552 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 190000000000000006364111469391636800465571396785379280504998912981509868379716200323128115249678998448553219208809025658820834125106841540316300816855815036957709089450163691323392 binary64)) (pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7548785066802179/431359146674410236714672241392314090778194310760649159697657763987456 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 7548785066802179/431359146674410236714672241392314090778194310760649159697657763987456 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 18500000000000001326515528856118709499189173587193619563203030027870830436603239197790903729406958111819908389287495204814218322087696297758769814497440667877670401432246318046823106924035178496 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 18500000000000001326515528856118709499189173587193619563203030027870830436603239197790903729406958111819908389287495204814218322087696297758769814497440667877670401432246318046823106924035178496 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 1800000000000000098948217486616420690110293681291206783925489232159862801485652853510527459077704553512813339997251871140538313039388899041893541449142923046752364560243159124418911144144535552 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 1800000000000000098948217486616420690110293681291206783925489232159862801485652853510527459077704553512813339997251871140538313039388899041893541449142923046752364560243159124418911144144535552 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 190000000000000006364111469391636800465571396785379280504998912981509868379716200323128115249678998448553219208809025658820834125106841540316300816855815036957709089450163691323392 binary64)) (pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))

soundness983.0ms (8.3%)

Memory
12.2MiB live, 1 045.8MiB allocated
Rules
11 826×accelerator-lowering-fma.f32
11 826×accelerator-lowering-fma.f64
11 382×accelerator-lowering-fma.f32
11 382×accelerator-lowering-fma.f64
6 430×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01338
18035
248833
3445133
0857233
027120
1153119
2962119
08366119
039179
1227167
21603164
08474162
01201122
13211103
29541013
33225986
45231908
08739896
030132
1172127
21123127
08285127
03085141
19884921
233634637
080874580
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 512 to 335 computations (34.6% saved)

preprocess71.0ms (0.6%)

Memory
29.2MiB live, 146.1MiB allocated
Compiler

Compiled 364 to 138 computations (62.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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