Average Error: 0.5 → 0.4
Time: 11.1s
Precision: binary64
Cost: 32896
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \]
↓
\[\frac{1}{\frac{\sqrt{k}}{\sqrt{\frac{2}{\frac{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{k}}{\pi \cdot n}}}}} \]
(FPCore (k n)
 :precision binary64
 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
↓
(FPCore (k n)
 :precision binary64
 (/ 1.0 (/ (sqrt k) (sqrt (/ 2.0 (/ (pow (* 2.0 (* PI n)) k) (* PI n)))))))
double code(double k, double n) {
	return (1.0 / sqrt(k)) * pow(((2.0 * ((double) M_PI)) * n), ((1.0 - k) / 2.0));
}
↓
double code(double k, double n) {
	return 1.0 / (sqrt(k) / sqrt((2.0 / (pow((2.0 * (((double) M_PI) * n)), k) / (((double) M_PI) * n)))));
}

public static double code(double k, double n) {
	return (1.0 / Math.sqrt(k)) * Math.pow(((2.0 * Math.PI) * n), ((1.0 - k) / 2.0));
}
↓
public static double code(double k, double n) {
	return 1.0 / (Math.sqrt(k) / Math.sqrt((2.0 / (Math.pow((2.0 * (Math.PI * n)), k) / (Math.PI * n)))));
}

def code(k, n):
	return (1.0 / math.sqrt(k)) * math.pow(((2.0 * math.pi) * n), ((1.0 - k) / 2.0))
↓
def code(k, n):
	return 1.0 / (math.sqrt(k) / math.sqrt((2.0 / (math.pow((2.0 * (math.pi * n)), k) / (math.pi * n)))))

function code(k, n)
	return Float64(Float64(1.0 / sqrt(k)) * (Float64(Float64(2.0 * pi) * n) ^ Float64(Float64(1.0 - k) / 2.0)))
end
↓
function code(k, n)
	return Float64(1.0 / Float64(sqrt(k) / sqrt(Float64(2.0 / Float64((Float64(2.0 * Float64(pi * n)) ^ k) / Float64(pi * n))))))
end

function tmp = code(k, n)
	tmp = (1.0 / sqrt(k)) * (((2.0 * pi) * n) ^ ((1.0 - k) / 2.0));
end
↓
function tmp = code(k, n)
	tmp = 1.0 / (sqrt(k) / sqrt((2.0 / (((2.0 * (pi * n)) ^ k) / (pi * n)))));
end

code[k_, n_] := N[(N[(1.0 / N[Sqrt[k], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(2.0 * Pi), $MachinePrecision] * n), $MachinePrecision], N[(N[(1.0 - k), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[k_, n_] := N[(1.0 / N[(N[Sqrt[k], $MachinePrecision] / N[Sqrt[N[(2.0 / N[(N[Power[N[(2.0 * N[(Pi * n), $MachinePrecision]), $MachinePrecision], k], $MachinePrecision] / N[(Pi * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\frac{\sqrt{k}}{\sqrt{\frac{2}{\frac{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{k}}{\pi \cdot n}}}}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \]

  2. Applied egg-rr0.5

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{k}}{\sqrt{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{\left(1 - k\right)}}}}} \]

  3. Applied egg-rr0.4

    \[\leadsto \frac{1}{\frac{\sqrt{k}}{\sqrt{\color{blue}{\frac{2}{\frac{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{k}}{\pi \cdot n}}}}}} \]

  4. Final simplification0.4

    \[\leadsto \frac{1}{\frac{\sqrt{k}}{\sqrt{\frac{2}{\frac{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{k}}{\pi \cdot n}}}}} \]

Alternatives

Alternative 1
Error0.3
Cost32832
\[{k}^{-0.5} \cdot \sqrt{2 \cdot \left(n \cdot \frac{\pi}{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{k}}\right)} \]
Alternative 2
Error0.6
Cost19972
\[\begin{array}{l} \mathbf{if}\;k \leq 1.687059219944924 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{n} \cdot \sqrt{2 \cdot \frac{\pi}{k}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{k}{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{\left(1 - k\right)}}\right)}^{-0.5}\\ \end{array} \]
Alternative 3
Error0.6
Cost19908
\[\begin{array}{l} \mathbf{if}\;k \leq 1.3099901661145611 \cdot 10^{-42}:\\ \;\;\;\;\sqrt{n} \cdot \sqrt{2 \cdot \frac{\pi}{k}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{\left(1 - k\right)}}{k}}\\ \end{array} \]
Alternative 4
Error0.4
Cost19904
\[\frac{{\left(\pi \cdot \left(2 \cdot n\right)\right)}^{\left(0.5 + k \cdot -0.5\right)}}{\sqrt{k}} \]
Alternative 5
Error18.1
Cost19844
\[\begin{array}{l} t_0 := 2 \cdot \frac{\pi}{k}\\ \mathbf{if}\;k \leq 1.32 \cdot 10^{+143}:\\ \;\;\;\;\sqrt{n} \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(n \cdot t_0\right)}^{3}\right)}^{0.16666666666666666}\\ \end{array} \]
Alternative 6
Error22.1
Cost19584
\[\sqrt{n} \cdot \sqrt{2 \cdot \frac{\pi}{k}} \]
Alternative 7
Error31.8
Cost13248
\[{\left(\frac{k}{\frac{n}{\frac{0.5}{\pi}}}\right)}^{-0.5} \]
Alternative 8
Error32.4
Cost13184
\[\sqrt{n \cdot \left(2 \cdot \frac{\pi}{k}\right)} \]
Alternative 9
Error32.4
Cost13184
\[\sqrt{\left(2 \cdot \pi\right) \cdot \frac{n}{k}} \]
Alternative 10
Error32.4
Cost13184
\[\sqrt{\frac{2 \cdot \pi}{\frac{k}{n}}} \]

Error

Reproduce

herbie shell --seed 2022320 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))