Timeout for init-K

Specification

\[\left(c > 0 \land ecc > 0\right) \land ecc < 1\]

Math

\[\begin{array}{l} t_0 := ecc \cdot \sin phi0\\ \log \tan \left(\frac{\pi}{4} + 0.5 \cdot phip0\right) - c \cdot \left(\log \tan \left(\frac{\pi}{4} + 0.5 \cdot phi0\right) - hlf\_e \cdot \log \left(\frac{1 + t\_0}{1 - t\_0}\right)\right) \end{array} \]

FPCore

(FPCore (phi0 phip0 c hlf_e ecc)
  :precision binary64
  :pre (and (and (> c 0.0) (> ecc 0.0)) (< ecc 1.0))
  (let* ((t_0 (* ecc (sin phi0))))
  (-
   (log (tan (+ (/ PI 4.0) (* 0.5 phip0))))
   (*
    c
    (-
     (log (tan (+ (/ PI 4.0) (* 0.5 phi0))))
     (* hlf_e (log (/ (+ 1.0 t_0) (- 1.0 t_0)))))))))

C

double code(double phi0, double phip0, double c, double hlf_e, double ecc) {
	double t_0 = ecc * sin(phi0);
	return log(tan(((((double) M_PI) / 4.0) + (0.5 * phip0)))) - (c * (log(tan(((((double) M_PI) / 4.0) + (0.5 * phi0)))) - (hlf_e * log(((1.0 + t_0) / (1.0 - t_0))))));
}

Java

public static double code(double phi0, double phip0, double c, double hlf_e, double ecc) {
	double t_0 = ecc * Math.sin(phi0);
	return Math.log(Math.tan(((Math.PI / 4.0) + (0.5 * phip0)))) - (c * (Math.log(Math.tan(((Math.PI / 4.0) + (0.5 * phi0)))) - (hlf_e * Math.log(((1.0 + t_0) / (1.0 - t_0))))));
}

Python

def code(phi0, phip0, c, hlf_e, ecc):
	t_0 = ecc * math.sin(phi0)
	return math.log(math.tan(((math.pi / 4.0) + (0.5 * phip0)))) - (c * (math.log(math.tan(((math.pi / 4.0) + (0.5 * phi0)))) - (hlf_e * math.log(((1.0 + t_0) / (1.0 - t_0))))))

Julia

function code(phi0, phip0, c, hlf_e, ecc)
	t_0 = Float64(ecc * sin(phi0))
	return Float64(log(tan(Float64(Float64(pi / 4.0) + Float64(0.5 * phip0)))) - Float64(c * Float64(log(tan(Float64(Float64(pi / 4.0) + Float64(0.5 * phi0)))) - Float64(hlf_e * log(Float64(Float64(1.0 + t_0) / Float64(1.0 - t_0)))))))
end

MATLAB

function tmp = code(phi0, phip0, c, hlf_e, ecc)
	t_0 = ecc * sin(phi0);
	tmp = log(tan(((pi / 4.0) + (0.5 * phip0)))) - (c * (log(tan(((pi / 4.0) + (0.5 * phi0)))) - (hlf_e * log(((1.0 + t_0) / (1.0 - t_0))))));
end

Wolfram

code[phi0_, phip0_, c_, hlf$95$e_, ecc_] := Block[{t$95$0 = N[(ecc * N[Sin[phi0], $MachinePrecision]), $MachinePrecision]}, N[(N[Log[N[Tan[N[(N[(Pi / 4.0), $MachinePrecision] + N[(0.5 * phip0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - N[(c * N[(N[Log[N[Tan[N[(N[(Pi / 4.0), $MachinePrecision] + N[(0.5 * phi0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - N[(hlf$95$e * N[Log[N[(N[(1.0 + t$95$0), $MachinePrecision] / N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(phi0, phip0, c, hlf_e, ecc):
	phi0 in [-inf, +inf],
	phip0 in [-inf, +inf],
	c in [0, +inf],
	hlf_e in [-inf, +inf],
	ecc in [0, 1]
code: THEORY
BEGIN
f(phi0, phip0, c, hlf_e, ecc: real): real =
	LET t_0 = (ecc * (sin(phi0))) IN
	(ln((tan((((4 * atan(1)) / (4)) + ((5e-1) * phip0)))))) - (c * ((ln((tan((((4 * atan(1)) / (4)) + ((5e-1) * phi0)))))) - (hlf_e * (ln((((1) + t_0) / ((1) - t_0)))))))
END code