Migdal et al, Equation (51)

Time bar (total: 10.3s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze117.0ms (1.1%)

Memory
15.8MiB live, 159.0MiB allocated; 26ms collecting garbage
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)

sample3.9s (37.9%)

Memory
80.0MiB live, 5 559.2MiB allocated; 955ms collecting garbage
Samples
1.2s8 256×0valid
1.1s4 401×1invalid
728.0ms1 499×2invalid
28.0ms357×0invalid
26.0ms226×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.2s
ival-pow: 559.0ms (26% of total)
ival-mult: 487.0ms (22.6% of total)
ival-div: 387.0ms (18% of total)
ival-sqrt: 271.0ms (12.6% of total)
adjust: 171.0ms (7.9% of total)
ival-sub: 145.0ms (6.7% of total)
ival-pi: 94.0ms (4.4% of total)
exact: 19.0ms (0.9% of total)
ival-true: 12.0ms (0.6% of total)
ival-assert: 7.0ms (0.3% of total)
Bogosity

explain193.0ms (1.9%)

Memory
60.6MiB live, 424.2MiB allocated; 68ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
190(3.9341877664839457e-199 9.011407498142887e-249)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)))sensitivity9121
Confusion
Predicted +Predicted -
+10
-90165
Precision
0.01098901098901099
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+100
-9021144
Precision?
0.008928571428571428
Recall?
1.0
Freqs
test
numberfreq
0165
191
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
92.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-sqrt: 21.0ms (40% of total)
ival-pow: 10.0ms (19% of total)
ival-mult: 9.0ms (17.1% of total)
ival-div: 7.0ms (13.3% of total)
ival-sub: 3.0ms (5.7% of total)
ival-pi: 2.0ms (3.8% of total)
exact: 1.0ms (1.9% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess44.0ms (0.4%)

Memory
5.8MiB live, 93.6MiB allocated; 18ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03188
17176
214574
322774
429674
536374
642874
750174
852874
954174
1054774
01316
02216
13714
25014
36714
48014
59814
613214
720214
822714
924714
1025714
025714
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.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))))
Outputs
(*.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 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(*.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 16 to 13 computations (18.8% saved)

simplify0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series99.0ms (1%)

Memory
3.4MiB live, 141.5MiB allocated; 47ms collecting garbage
Counts
13 → 34
Calls
Call 1
Inputs
(*.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) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(* (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))
(sqrt k)
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)))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
n
(* (sqrt (/ 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 (/ 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))))
Calls

6 calls:

TimeVariablePointExpression
50.0ms
n
@0
((* (/ 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))
27.0ms
n
@-inf
((* (/ 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))
9.0ms
k
@inf
((* (/ 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))
8.0ms
n
@inf
((* (/ 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))
3.0ms
k
@-inf
((* (/ 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))

simplify197.0ms (1.9%)

Memory
5.6MiB live, 192.2MiB allocated; 111ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0133550
1412536
21446500
34266499
08089486
Stop Event
1×iter limit
1×node limit
Counts
34 → 32
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))
(sqrt k)
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)))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
n
(* (sqrt (/ 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 (/ 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))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(/ (+ (* -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)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.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)
(fma.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) 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 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
k
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(+ (* 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)))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (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)))
(fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 k))
(-.f64 #s(literal 1 binary64) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)
(* -1 k)
(neg.f64 k)
(* k (- (/ 1 k) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal -1/2 binary64)) k)
(* -1 (* k (- 1 (/ 1 k))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)) (neg.f64 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))
(* 2 (* n (PI)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
n
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))

rewrite173.0ms (1.7%)

Memory
7.0MiB live, 289.8MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01354
02254
18351
244651
3400743
0892143
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
13 → 480
Calls
Call 1
Inputs
(*.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) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (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))) (pow.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.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))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.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))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 0 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
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(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(fma.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sinh.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) (log.f64 (*.f64 #s(literal 0 binary64) n)))) (pow.f64 k #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) (log.f64 (*.f64 #s(literal 0 binary64) n))))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) (log.f64 (*.f64 #s(literal 0 binary64) n)))))
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(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(-.f64 (pow.f64 (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (pow.f64 (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 k (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.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 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 k k k) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 k k k)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 k k k) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 k k k) (-.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))))) (+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (+.f64 k #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (*.f64 (+.f64 k #s(literal 1 binary64)) (*.f64 k k))) (*.f64 (+.f64 k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 4 binary64))) (*.f64 (fma.f64 k k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (*.f64 (+.f64 (fma.f64 k k (pow.f64 k #s(literal 4 binary64))) #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (*.f64 (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 9 binary64))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k)) (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 k (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))))
(-.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval81.0ms (0.8%)

Memory
-25.4MiB live, 218.5MiB allocated; 19ms collecting garbage
Compiler

Compiled 11 951 to 2 097 computations (82.5% saved)

prune30.0ms (0.3%)

Memory
20.9MiB live, 110.0MiB allocated; 9ms collecting garbage
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New49319512
Fresh000
Picked101
Done000
Total49419513
Accuracy
100.0%
Counts
513 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
25.2%
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.6%
(*.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))))
▶76.1%
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶56.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
47.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
60.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
56.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
47.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))))
47.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
▶76.2%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.4%
(*.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.4%
(*.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))))
50.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))))
50.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
49.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
Compiler

Compiled 1 256 to 870 computations (30.7% saved)

simplify0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

series238.0ms (2.3%)

Memory
-18.8MiB live, 401.0MiB allocated; 109ms collecting garbage
Counts
32 → 81
Calls
Call 1
Inputs
(*.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 k #s(literal -1/2 binary64))
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)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(* (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))
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)))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(sqrt k)
(* -1/2 k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* k (+ (* -1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(sqrt (* n (PI)))
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* -1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(* (sqrt (/ 1 k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k))))))
(exp (* 1/2 (* (log 2) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (- 1 k)))))
(exp (* 1/2 (* (log (* n (PI))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log 2) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))))
(exp (* 1/2 (* (log 2) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (* (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
n
(* n (PI))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))
(* (sqrt (/ 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 (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 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))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Calls

6 calls:

TimeVariablePointExpression
100.0ms
k
@-inf
((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) k -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k))) (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (PI)) (/ (- 1 k) 2)) (* n (PI)) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))))
61.0ms
n
@0
((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) k -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k))) (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (PI)) (/ (- 1 k) 2)) (* n (PI)) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))))
33.0ms
n
@-inf
((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) k -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k))) (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (PI)) (/ (- 1 k) 2)) (* n (PI)) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))))
24.0ms
n
@inf
((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) k -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k))) (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (PI)) (/ (- 1 k) 2)) (* n (PI)) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))))
15.0ms
k
@0
((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) k -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k))) (pow 2 (/ (- 1 k) 2)) (/ (pow (* n (PI)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (PI)) (/ (- 1 k) 2)) (* n (PI)) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))))

simplify253.0ms (2.5%)

Memory
-5.8MiB live, 277.1MiB allocated; 33ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03331749
111701626
249541572
085351516
Stop Event
1×iter limit
1×node limit
Counts
81 → 79
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))
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)))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(sqrt k)
(* -1/2 k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* k (+ (* -1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(sqrt (* n (PI)))
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* -1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(* (sqrt (/ 1 k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k))))))
(exp (* 1/2 (* (log 2) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (- 1 k)))))
(exp (* 1/2 (* (log (* n (PI))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log 2) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))))
(exp (* 1/2 (* (log 2) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (* (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
n
(* n (PI))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))
(* (sqrt (/ 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 (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 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))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.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 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #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 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
k
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 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)))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(+ (* 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)))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal -1/48 binary64)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 k))
(-.f64 #s(literal 1 binary64) k)
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(sqrt k)
(sqrt.f64 k)
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (log.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (fma.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (log.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* k (+ (* -1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)) k (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal 1/8 binary64))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k)
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 (PI.f64) n))
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* -1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal -1/48 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64)) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))))))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (log.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (sqrt.f64 (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)
(* -1 k)
(neg.f64 k)
(* k (- (/ 1 k) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k)
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k))))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log 2) (- 1 k))))
(sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* n (PI))) (- 1 k))))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log 2) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k)))
(* -1 (* k (- 1 (/ 1 k))))
(*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log 2) (+ 1 (* -1 k)))))
(sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (* (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))))
(*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) (sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* 2 (* n (PI)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
n
(* n (PI))
(*.f64 (PI.f64) n)
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))))
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n)) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n))) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))))
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n)) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n))) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1 binary64))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))

rewrite307.0ms (3%)

Memory
19.2MiB live, 297.8MiB allocated; 37ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
041238
067224
1183217
2828217
37639217
08042217
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
32 → 1 540
Calls
Call 1
Inputs
(*.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 k #s(literal -1/2 binary64))
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)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/8 binary64))) (pow.f64 k #s(literal -1/8 binary64)))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.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 4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (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 4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(fma.f64 (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(fma.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))))
(fma.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(+.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
(+.f64 (cosh.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) (sinh.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))

eval482.0ms (4.7%)

Memory
12.0MiB live, 514.3MiB allocated; 78ms collecting garbage
Compiler

Compiled 63 127 to 6 351 computations (89.9% saved)

prune100.0ms (1%)

Memory
-29.8MiB live, 132.9MiB allocated; 33ms collecting garbage
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New2 151162 167
Fresh12214
Picked505
Done000
Total2 168182 186
Accuracy
100.0%
Counts
2 186 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶99.7%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
47.4%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
▶47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
▶47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
▶34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
▶33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
Compiler

Compiled 942 to 762 computations (19.1% saved)

simplify0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

series68.0ms (0.7%)

Memory
-8.6MiB live, 80.8MiB allocated; 16ms collecting garbage
Counts
32 → 52
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (PI.f64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))
(sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
Outputs
(* (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 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* 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)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(+ (sqrt k) (* k (+ (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))))))
(+ (sqrt k) (* k (+ (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* 1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))))))))
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))
(* 1/2 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)
(/ (+ (* 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)
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt k) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))
(exp (* 1/2 (* k (log (* 2 (* n (PI)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* -1 (* (sqrt k) (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* 2 (* n (PI)))
n
(* (sqrt k) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* n (PI))
(sqrt (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
Calls

6 calls:

TimeVariablePointExpression
25.0ms
n
@-inf
((/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (* k 1/2)) (* k 1/2) k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (* (PI) 2))) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k))) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k)) (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k) (* (* (sqrt (PI)) (sqrt (PI))) n) (* (sqrt (PI)) (sqrt (PI))) (sqrt (PI)))
11.0ms
n
@0
((/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (* k 1/2)) (* k 1/2) k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (* (PI) 2))) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k))) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k)) (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k) (* (* (sqrt (PI)) (sqrt (PI))) n) (* (sqrt (PI)) (sqrt (PI))) (sqrt (PI)))
11.0ms
n
@inf
((/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (* k 1/2)) (* k 1/2) k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (* (PI) 2))) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k))) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k)) (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k) (* (* (sqrt (PI)) (sqrt (PI))) n) (* (sqrt (PI)) (sqrt (PI))) (sqrt (PI)))
10.0ms
k
@-inf
((/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (* k 1/2)) (* k 1/2) k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (* (PI) 2))) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k))) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k)) (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k) (* (* (sqrt (PI)) (sqrt (PI))) n) (* (sqrt (PI)) (sqrt (PI))) (sqrt (PI)))
5.0ms
k
@0
((/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (* k 1/2)) (* k 1/2) k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (* (PI) 2))) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k))) (sqrt (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k)) (/ (* (* (sqrt (PI)) (sqrt (PI))) n) k) (* (* (sqrt (PI)) (sqrt (PI))) n) (* (sqrt (PI)) (sqrt (PI))) (sqrt (PI)))

simplify208.0ms (2%)

Memory
28.8MiB live, 210.1MiB allocated; 41ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0205955
1698935
22843882
08349858
Stop Event
1×iter limit
1×node limit
Counts
52 → 50
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 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* 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)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(+ (sqrt k) (* k (+ (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))))))
(+ (sqrt k) (* k (+ (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* 1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))))))))
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))
(* 1/2 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)
(/ (+ (* 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)
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt k) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))
(exp (* 1/2 (* k (log (* 2 (* n (PI)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* -1 (* (sqrt k) (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* 2 (* n (PI)))
n
(* (sqrt k) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* n (PI))
(sqrt (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(/ (+ (* -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)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k)) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt k)
(sqrt.f64 k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))
(+ (sqrt k) (* k (+ (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))))))
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal 1/8 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 k)))) k (sqrt.f64 k))
(+ (sqrt k) (* k (+ (* 1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* 1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))))))))
(fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal 1/48 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k)))) k (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 k)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))) k (sqrt.f64 k))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64))
(+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1/2 binary64))) k #s(literal 1 binary64))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))
(fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/48 binary64) k) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1/8 binary64))) k (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))) k #s(literal 1 binary64))
(* 1/2 k)
(*.f64 #s(literal 1/2 binary64) 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 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #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 (fma.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))))) k)) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* 2 (/ (* n (PI)) k))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt k) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k)) (sqrt.f64 k))
(exp (* 1/2 (* k (log (* 2 (* n (PI)))))))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt k) (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (pow (sqrt -1) 2))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k)) (sqrt.f64 k))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
n
(* (sqrt k) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 k))
(exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* n (PI))
(*.f64 (PI.f64) n)
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 (PI.f64) n))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 k))
(exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(* (sqrt k) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 k))
(exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 (PI.f64) n))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))

rewrite207.0ms (2%)

Memory
19.9MiB live, 356.6MiB allocated; 60ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042271
066238
1197223
2885184
08619184
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
32 → 1 277
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (PI.f64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))
(sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
Outputs
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)) (/.f64 #s(literal 0 binary64) (pow.f64 #s(literal 0 binary64) k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) (pow.f64 #s(literal 0 binary64) k)) (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (pow.f64 #s(literal 0 binary64) k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 n) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (pow.f64 (sqrt.f64 n) k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 #s(literal 0 binary64) k)))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 #s(literal 0 binary64) k)) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 n) k)))
(*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 n) k)) (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)) (pow.f64 #s(literal 0 binary64) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (sqrt.f64 n) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 0 binary64) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 #s(literal 0 binary64) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 n) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (sqrt.f64 n) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 #s(literal 0 binary64) k)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 #s(literal 0 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 n) k)))
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(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (fabs.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(pow.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(neg.f64 (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(fabs.f64 (sqrt.f64 (PI.f64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (PI.f64))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (PI.f64)))) (sinh.f64 (log.f64 (sqrt.f64 (PI.f64)))))

eval303.0ms (2.9%)

Memory
9.4MiB live, 625.2MiB allocated; 97ms collecting garbage
Compiler

Compiled 51 373 to 6 430 computations (87.5% saved)

prune108.0ms (1%)

Memory
-30.5MiB live, 205.9MiB allocated; 31ms collecting garbage
Pruning

27 alts after pruning (24 fresh and 3 done)

PrunedKeptTotal
New1 760201 780
Fresh9413
Picked235
Done000
Total1 771271 798
Accuracy
100.0%
Counts
1 798 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓99.7%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
47.4%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
34.3%
#s(approx (/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
3.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
✓47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
▶99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
✓47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
▶47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
▶47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
▶34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
▶30.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
33.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
Compiler

Compiled 1 334 to 1 074 computations (19.5% saved)

simplify0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

series89.0ms (0.9%)

Memory
-9.4MiB live, 124.8MiB allocated; 58ms collecting garbage
Counts
38 → 52
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (PI.f64) n)
(PI.f64)
n
#s(literal 2 binary64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k))
(/.f64 (*.f64 #s(literal 0 binary64) n) k)
(*.f64 #s(literal 0 binary64) n)
#s(literal 0 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(sqrt.f64 n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
#s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(* (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 (* 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)))
1/2
(+ 1/2 (* -1/2 k))
k
(sqrt (/ 1 k))
(/ 1 k)
0
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(/ n k)
(sqrt (/ (PI) k))
(/ (PI) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* n (PI))
n
(sqrt n)
(sqrt (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
Calls

6 calls:

TimeVariablePointExpression
52.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* 0 n) k)) (/ (* 0 n) k) (* 0 n) 0 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (sqrt 2) (sqrt (* (/ n k) (PI))) (* (/ n k) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ (PI) k)) (sqrt n))) (* (sqrt (/ (PI) k)) (sqrt n)) (sqrt (/ (PI) k)) (/ (PI) k) (sqrt n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (* n (PI)) (/ (sqrt 2) (sqrt k)) (* (sqrt (/ 1 k)) (sqrt 2)))
13.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* 0 n) k)) (/ (* 0 n) k) (* 0 n) 0 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (sqrt 2) (sqrt (* (/ n k) (PI))) (* (/ n k) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ (PI) k)) (sqrt n))) (* (sqrt (/ (PI) k)) (sqrt n)) (sqrt (/ (PI) k)) (/ (PI) k) (sqrt n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (* n (PI)) (/ (sqrt 2) (sqrt k)) (* (sqrt (/ 1 k)) (sqrt 2)))
12.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* 0 n) k)) (/ (* 0 n) k) (* 0 n) 0 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (sqrt 2) (sqrt (* (/ n k) (PI))) (* (/ n k) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ (PI) k)) (sqrt n))) (* (sqrt (/ (PI) k)) (sqrt n)) (sqrt (/ (PI) k)) (/ (PI) k) (sqrt n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (* n (PI)) (/ (sqrt 2) (sqrt k)) (* (sqrt (/ 1 k)) (sqrt 2)))
5.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* 0 n) k)) (/ (* 0 n) k) (* 0 n) 0 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (sqrt 2) (sqrt (* (/ n k) (PI))) (* (/ n k) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ (PI) k)) (sqrt n))) (* (sqrt (/ (PI) k)) (sqrt n)) (sqrt (/ (PI) k)) (/ (PI) k) (sqrt n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (* n (PI)) (/ (sqrt 2) (sqrt k)) (* (sqrt (/ 1 k)) (sqrt 2)))
3.0ms
k
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* 0 n) k)) (/ (* 0 n) k) (* 0 n) 0 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (sqrt 2) (sqrt (* (/ n k) (PI))) (* (/ n k) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ (PI) k)) (sqrt n))) (* (sqrt (/ (PI) k)) (sqrt n)) (sqrt (/ (PI) k)) (/ (PI) k) (sqrt n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (PI))) (/ (sqrt 2) (sqrt k))) (sqrt (* n (PI))) (* n (PI)) (/ (sqrt 2) (sqrt k)) (* (sqrt (/ 1 k)) (sqrt 2)))

simplify202.0ms (2%)

Memory
-16.8MiB live, 212.6MiB allocated; 27ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161726
1512692
21878641
35633632
08486619
Stop Event
1×iter limit
1×node limit
Counts
52 → 50
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 (* 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)))
1/2
(+ 1/2 (* -1/2 k))
k
(sqrt (/ 1 k))
(/ 1 k)
0
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(/ n k)
(sqrt (/ (PI) k))
(/ (PI) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* n (PI))
n
(sqrt n)
(sqrt (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
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)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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)
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))) #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.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)
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))) #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* 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)))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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)))
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
k
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
0
#s(literal 0 binary64)
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ n k)
(/.f64 n k)
(sqrt (/ (PI) k))
(sqrt.f64 (/.f64 (PI.f64) k))
(/ (PI) k)
(/.f64 (PI.f64) k)
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) k) #s(literal -1 binary64) #s(literal -1/2 binary64)) k)
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ 1 k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* n (PI))
(*.f64 n (PI.f64))
n
(sqrt n)
(sqrt.f64 n)
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))

rewrite171.0ms (1.7%)

Memory
0.7MiB live, 289.3MiB allocated; 37ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049305
075278
1222254
2998218
08490218
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
38 → 1 495
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (PI.f64) n)
(PI.f64)
n
#s(literal 2 binary64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k))
(/.f64 (*.f64 #s(literal 0 binary64) n) k)
(*.f64 #s(literal 0 binary64) n)
#s(literal 0 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(sqrt.f64 n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
#s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))))
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(*.f64 (*.f64 (sqrt.f64 n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (*.f64 (pow.f64 n #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 n)))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (log.f64 n) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 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)))
(*.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 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 n (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) n))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) n (*.f64 (sinh.f64 (log.f64 (PI.f64))) n))
(fma.f64 n (cosh.f64 (log.f64 (PI.f64))) (*.f64 n (sinh.f64 (log.f64 (PI.f64)))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) n) (*.f64 (sinh.f64 (log.f64 (PI.f64))) n))
(+.f64 (*.f64 n (cosh.f64 (log.f64 (PI.f64)))) (*.f64 n (sinh.f64 (log.f64 (PI.f64)))))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
#s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 #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 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (sqrt.f64 k)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
(hypot.f64 (neg.f64 (pow.f64 k #s(literal -1/2 binary64))) (neg.f64 (pow.f64 k #s(literal -1/2 binary64))))
(hypot.f64 (neg.f64 (pow.f64 k #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(hypot.f64 (neg.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(hypot.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 k #s(literal -1/2 binary64))))
(hypot.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(hypot.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 k #s(literal -1/2 binary64)))
(hypot.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (pow.f64 k #s(literal -1/2 binary64))))
(hypot.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(hypot.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (-.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64)))

eval949.0ms (9.2%)

Memory
-44.9MiB live, 635.9MiB allocated; 1.1s collecting garbage
Compiler

Compiled 56 173 to 6 317 computations (88.8% saved)

prune116.0ms (1.1%)

Memory
-15.5MiB live, 177.5MiB allocated; 18ms collecting garbage
Pruning

22 alts after pruning (18 fresh and 4 done)

PrunedKeptTotal
New1 54581 553
Fresh91019
Picked325
Done123
Total1 558221 580
Accuracy
100.0%
Counts
1 580 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓99.7%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
47.4%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
3.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
✓47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
✓99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
47.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
5.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
47.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
4.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
4.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
✓34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
33.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
5.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
4.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
30.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
Compiler

Compiled 2 346 to 752 computations (67.9% saved)

regimes119.0ms (1.2%)

Memory
16.5MiB live, 163.5MiB allocated; 63ms collecting garbage
Counts
64 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.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 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))) (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)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
Calls

4 calls:

61.0ms
(*.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))))
19.0ms
k
19.0ms
n
16.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%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))))
99.7%1k
99.7%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes59.0ms (0.6%)

Memory
-8.3MiB live, 130.6MiB allocated; 8ms collecting garbage
Counts
49 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.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))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Calls

4 calls:

17.0ms
n
15.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms
k
13.0ms
(*.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%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
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%1k
99.6%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes59.0ms (0.6%)

Memory
9.4MiB live, 147.4MiB allocated; 19ms collecting garbage
Counts
46 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
Calls

4 calls:

17.0ms
k
14.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms
(*.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))))
12.0ms
n
Results
AccuracySegmentsBranch
62.6%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.8%3(*.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))))
98.8%2k
62.6%3n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes27.0ms (0.3%)

Memory
17.8MiB live, 62.3MiB allocated; 6ms collecting garbage
Counts
43 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* n (* (PI) 2))) (* (pow (* n (* (PI) 2)) (* k 1/2)) (sqrt k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 n) (PI.f64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (/ (sqrt 2) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(approx (/ (sqrt 2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
Calls

2 calls:

13.0ms
(*.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))))
11.0ms
k
Results
AccuracySegmentsBranch
75.8%2(*.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))))
75.7%2k
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes15.0ms (0.1%)

Memory
-16.1MiB live, 37.7MiB allocated; 9ms collecting garbage
Counts
16 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
Calls

2 calls:

9.0ms
k
4.0ms
(*.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
62.6%2k
62.7%2(*.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 17 to 15 computations (11.8% saved)

regimes5.0ms (0.1%)

Memory
19.6MiB live, 19.6MiB allocated; 0ms collecting garbage
Counts
15 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
Calls

1 calls:

4.0ms
(*.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
62.7%2(*.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 16 to 13 computations (18.8% saved)

regimes11.0ms (0.1%)

Memory
-25.6MiB live, 20.8MiB allocated; 3ms collecting garbage
Counts
13 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
Calls

2 calls:

6.0ms
(*.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))))
4.0ms
k
Results
AccuracySegmentsBranch
61.9%2k
62.0%2(*.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 17 to 15 computations (11.8% saved)

regimes4.0ms (0%)

Memory
8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Counts
10 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))
Calls

1 calls:

3.0ms
(*.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
62.0%2(*.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 16 to 13 computations (18.8% saved)

regimes3.0ms (0%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
Calls

1 calls:

2.0ms
(*.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
61.9%2(*.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 16 to 13 computations (18.8% saved)

regimes23.0ms (0.2%)

Memory
-25.8MiB live, 19.7MiB allocated; 4ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 0 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

4 calls:

2.0ms
k
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
(*.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
30.9%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
30.9%1n
32.9%2k
33.2%2(*.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 23 to 23 computations (0% saved)

regimes2.0ms (0%)

Memory
4.1MiB live, 4.1MiB allocated; 0ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
Calls

1 calls:

2.0ms
(*.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
33.0%2(*.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 16 to 13 computations (18.8% saved)

regimes5.0ms (0%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
Calls

4 calls:

1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
k
1.0ms
(*.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
30.9%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
30.9%1n
30.9%1k
30.9%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))))
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch23.0ms (0.2%)

Memory
27.1MiB live, 27.1MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
20.0ms
1.9466213115259886e-7
4.067031882229442
Samples
14.0ms144×0valid
Compiler

Compiled 415 to 369 computations (11.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-pow: 3.0ms (31.1% of total)
ival-div: 2.0ms (20.7% of total)
ival-mult: 2.0ms (20.7% of total)
ival-pi: 1.0ms (10.4% of total)
ival-sub: 1.0ms (10.4% of total)
ival-sqrt: 1.0ms (10.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4117553917220436e-122
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch32.0ms (0.3%)

Memory
-17.5MiB live, 28.0MiB allocated; 6ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
31.0ms
0.0
1.4117553917220436e-122
Samples
22.0ms224×0valid
Compiler

Compiled 663 to 578 computations (12.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify33.0ms (0.3%)

Memory
-23.0MiB live, 26.8MiB allocated; 14ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
095655
1117599
2135599
3156599
4173599
5192599
6228599
7299599
8334599
9371599
10383599
11385599
12387599
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.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)))) #s(literal 320786806109831/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))))
(if (<=.f64 (*.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)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.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)))) #s(literal 320786806109831/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 320786806109831/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 0 n) k)) #s(literal 0 binary64)))

derivations1.1s (11.2%)

Memory
8.1MiB live, 1 017.6MiB allocated; 184ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0161726
1512692
21878641
35633632
08486619
041238
067224
1183217
2828217
37639217
08042217
01354
02254
18351
244651
3400743
0892143
042271
066238
1197223
2885184
08619184
0133550
1412536
21446500
34266499
08089486
049305
075278
1222254
2998218
08490218
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 673 to 99 computations (85.3% saved)

preprocess81.0ms (0.8%)

Memory
3.8MiB live, 95.9MiB allocated; 5ms collecting garbage
Compiler

Compiled 1 378 to 224 computations (83.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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