Timeout for inverse-s

Specification

\[rho0 > 0 \land rho > 0\]

Math

\[2 \cdot \left(\tan^{-1} \left({\left(\frac{rho0}{rho}\right)}^{\left(\frac{1}{n}\right)} \cdot \tan \left(0.5 \cdot 1.37008346281555 + \frac{\pi}{4}\right)\right) - \frac{\pi}{4}\right) \]

FPCore

(FPCore (rho0 rho n)
  :precision binary64
  :pre (and (> rho0 0.0) (> rho 0.0))
  (*
 2.0
 (-
  (atan
   (*
    (pow (/ rho0 rho) (/ 1.0 n))
    (tan (+ (* 0.5 1.37008346281555) (/ PI 4.0)))))
  (/ PI 4.0))))

C

double code(double rho0, double rho, double n) {
	return 2.0 * (atan((pow((rho0 / rho), (1.0 / n)) * tan(((0.5 * 1.37008346281555) + (((double) M_PI) / 4.0))))) - (((double) M_PI) / 4.0));
}

Java

public static double code(double rho0, double rho, double n) {
	return 2.0 * (Math.atan((Math.pow((rho0 / rho), (1.0 / n)) * Math.tan(((0.5 * 1.37008346281555) + (Math.PI / 4.0))))) - (Math.PI / 4.0));
}

Python

def code(rho0, rho, n):
	return 2.0 * (math.atan((math.pow((rho0 / rho), (1.0 / n)) * math.tan(((0.5 * 1.37008346281555) + (math.pi / 4.0))))) - (math.pi / 4.0))

Julia

function code(rho0, rho, n)
	return Float64(2.0 * Float64(atan(Float64((Float64(rho0 / rho) ^ Float64(1.0 / n)) * tan(Float64(Float64(0.5 * 1.37008346281555) + Float64(pi / 4.0))))) - Float64(pi / 4.0)))
end

MATLAB

function tmp = code(rho0, rho, n)
	tmp = 2.0 * (atan((((rho0 / rho) ^ (1.0 / n)) * tan(((0.5 * 1.37008346281555) + (pi / 4.0))))) - (pi / 4.0));
end

Wolfram

code[rho0_, rho_, n_] := N[(2.0 * N[(N[ArcTan[N[(N[Power[N[(rho0 / rho), $MachinePrecision], N[(1.0 / n), $MachinePrecision]], $MachinePrecision] * N[Tan[N[(N[(0.5 * 1.37008346281555), $MachinePrecision] + N[(Pi / 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(Pi / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(rho0, rho, n):
	rho0 in [0, +inf],
	rho in [0, +inf],
	n in [-inf, +inf]
code: THEORY
BEGIN
f(rho0, rho, n: real): real =
	(2) * ((atan((((rho0 / rho) ^ ((1) / n)) * (tan((((5e-1) * (1370083462815550046087764712865464389324188232421875e-51)) + ((4 * atan(1)) / (4)))))))) - ((4 * atan(1)) / (4)))
END code