Equirectangular approximation to distance on a great circle

Percentage Accurate: 59.5% → 99.9%

Time: 25.4s

Alternatives: 15

Speedup: 1.5×

• 30.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\lambda_1 - \lambda_2\right) \cdot \cos \left(\frac{\phi_1 + \phi_2}{2}\right)\\ R \cdot \sqrt{t_0 \cdot t_0 + \left(\phi_1 - \phi_2\right) \cdot \left(\phi_1 - \phi_2\right)} \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
   (* R (sqrt (+ (* t_0 t_0) (* (- phi1 phi2) (- phi1 phi2)))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0));
	return R * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0d0))
    code = r * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))))
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = (lambda1 - lambda2) * Math.cos(((phi1 + phi2) / 2.0));
	return R * Math.sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = (lambda1 - lambda2) * math.cos(((phi1 + phi2) / 2.0))
	return R * math.sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))))

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(Float64(lambda1 - lambda2) * cos(Float64(Float64(phi1 + phi2) / 2.0)))
	return Float64(R * sqrt(Float64(Float64(t_0 * t_0) + Float64(Float64(phi1 - phi2) * Float64(phi1 - phi2)))))
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0));
	tmp = R * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(N[(lambda1 - lambda2), $MachinePrecision] * N[Cos[N[(N[(phi1 + phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(R * N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] + N[(N[(phi1 - phi2), $MachinePrecision] * N[(phi1 - phi2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Initial Program: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\lambda_1 - \lambda_2\right) \cdot \cos \left(\frac{\phi_1 + \phi_2}{2}\right)\\ R \cdot \sqrt{t_0 \cdot t_0 + \left(\phi_1 - \phi_2\right) \cdot \left(\phi_1 - \phi_2\right)} \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
   (* R (sqrt (+ (* t_0 t_0) (* (- phi1 phi2) (- phi1 phi2)))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0));
	return R * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0d0))
    code = r * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))))
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = (lambda1 - lambda2) * Math.cos(((phi1 + phi2) / 2.0));
	return R * Math.sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = (lambda1 - lambda2) * math.cos(((phi1 + phi2) / 2.0))
	return R * math.sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))))

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(Float64(lambda1 - lambda2) * cos(Float64(Float64(phi1 + phi2) / 2.0)))
	return Float64(R * sqrt(Float64(Float64(t_0 * t_0) + Float64(Float64(phi1 - phi2) * Float64(phi1 - phi2)))))
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = (lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0));
	tmp = R * sqrt(((t_0 * t_0) + ((phi1 - phi2) * (phi1 - phi2))));
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(N[(lambda1 - lambda2), $MachinePrecision] * N[Cos[N[(N[(phi1 + phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(R * N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] + N[(N[(phi1 - phi2), $MachinePrecision] * N[(phi1 - phi2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ R \cdot \mathsf{hypot}\left(\left(\cos \left(0.5 \cdot \phi_1\right) \cdot \cos \left(0.5 \cdot \phi_2\right) - \sin \left(0.5 \cdot \phi_1\right) \cdot \sin \left(0.5 \cdot \phi_2\right)\right) \cdot \left(\lambda_1 - \lambda_2\right), \phi_1 - \phi_2\right) \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (*
  R
  (hypot
   (*
    (-
     (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))
     (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
    (- lambda1 lambda2))
   (- phi1 phi2))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * hypot((((cos((0.5 * phi1)) * cos((0.5 * phi2))) - (sin((0.5 * phi1)) * sin((0.5 * phi2)))) * (lambda1 - lambda2)), (phi1 - phi2));
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * Math.hypot((((Math.cos((0.5 * phi1)) * Math.cos((0.5 * phi2))) - (Math.sin((0.5 * phi1)) * Math.sin((0.5 * phi2)))) * (lambda1 - lambda2)), (phi1 - phi2));
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	return R * math.hypot((((math.cos((0.5 * phi1)) * math.cos((0.5 * phi2))) - (math.sin((0.5 * phi1)) * math.sin((0.5 * phi2)))) * (lambda1 - lambda2)), (phi1 - phi2))

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	return Float64(R * hypot(Float64(Float64(Float64(cos(Float64(0.5 * phi1)) * cos(Float64(0.5 * phi2))) - Float64(sin(Float64(0.5 * phi1)) * sin(Float64(0.5 * phi2)))) * Float64(lambda1 - lambda2)), Float64(phi1 - phi2)))
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	tmp = R * hypot((((cos((0.5 * phi1)) * cos((0.5 * phi2))) - (sin((0.5 * phi1)) * sin((0.5 * phi2)))) * (lambda1 - lambda2)), (phi1 - phi2));
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := N[(R * N[Sqrt[N[(N[(N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(lambda1 - lambda2), $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\lambda_1 \leq -4.8 \cdot 10^{+215}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\left(\cos \left(0.5 \cdot \phi_1\right) \cdot \cos \left(0.5 \cdot \phi_2\right) - \sin \left(0.5 \cdot \phi_1\right) \cdot \sin \left(0.5 \cdot \phi_2\right)\right) \cdot \lambda_1, \phi_1 - \phi_2\right)\\ \mathbf{else}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\left(\lambda_1 - \lambda_2\right) \cdot \cos \left(\frac{\phi_1 + \phi_2}{2}\right), \phi_1 - \phi_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (if (<= lambda1 -4.8e+215)
   (*
    R
    (hypot
     (*
      (-
       (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))
       (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
      lambda1)
     (- phi1 phi2)))
   (*
    R
    (hypot
     (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
     (- phi1 phi2)))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (lambda1 <= -4.8e+215) {
		tmp = R * hypot((((cos((0.5 * phi1)) * cos((0.5 * phi2))) - (sin((0.5 * phi1)) * sin((0.5 * phi2)))) * lambda1), (phi1 - phi2));
	} else {
		tmp = R * hypot(((lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
	}
	return tmp;
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (lambda1 <= -4.8e+215) {
		tmp = R * Math.hypot((((Math.cos((0.5 * phi1)) * Math.cos((0.5 * phi2))) - (Math.sin((0.5 * phi1)) * Math.sin((0.5 * phi2)))) * lambda1), (phi1 - phi2));
	} else {
		tmp = R * Math.hypot(((lambda1 - lambda2) * Math.cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	tmp = 0
	if lambda1 <= -4.8e+215:
		tmp = R * math.hypot((((math.cos((0.5 * phi1)) * math.cos((0.5 * phi2))) - (math.sin((0.5 * phi1)) * math.sin((0.5 * phi2)))) * lambda1), (phi1 - phi2))
	else:
		tmp = R * math.hypot(((lambda1 - lambda2) * math.cos(((phi1 + phi2) / 2.0))), (phi1 - phi2))
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0
	if (lambda1 <= -4.8e+215)
		tmp = Float64(R * hypot(Float64(Float64(Float64(cos(Float64(0.5 * phi1)) * cos(Float64(0.5 * phi2))) - Float64(sin(Float64(0.5 * phi1)) * sin(Float64(0.5 * phi2)))) * lambda1), Float64(phi1 - phi2)));
	else
		tmp = Float64(R * hypot(Float64(Float64(lambda1 - lambda2) * cos(Float64(Float64(phi1 + phi2) / 2.0))), Float64(phi1 - phi2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0;
	if (lambda1 <= -4.8e+215)
		tmp = R * hypot((((cos((0.5 * phi1)) * cos((0.5 * phi2))) - (sin((0.5 * phi1)) * sin((0.5 * phi2)))) * lambda1), (phi1 - phi2));
	else
		tmp = R * hypot(((lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := If[LessEqual[lambda1, -4.8e+215], N[(R * N[Sqrt[N[(N[(N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * lambda1), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], N[(R * N[Sqrt[N[(N[(lambda1 - lambda2), $MachinePrecision] * N[Cos[N[(N[(phi1 + phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(0.5 \cdot \phi_1\right) \cdot \sin \left(0.5 \cdot \phi_2\right)\\ t_1 := \cos \left(0.5 \cdot \phi_1\right) \cdot \cos \left(0.5 \cdot \phi_2\right)\\ \mathbf{if}\;\lambda_2 \leq 4000000000000:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\left(t_1 - t_0\right) \cdot \lambda_1, \phi_1 - \phi_2\right)\\ \mathbf{else}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\lambda_2 \cdot \left(t_0 - t_1\right), \phi_1 - \phi_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
        (t_1 (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))))
   (if (<= lambda2 4000000000000.0)
     (* R (hypot (* (- t_1 t_0) lambda1) (- phi1 phi2)))
     (* R (hypot (* lambda2 (- t_0 t_1)) (- phi1 phi2))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = sin((0.5 * phi1)) * sin((0.5 * phi2));
	double t_1 = cos((0.5 * phi1)) * cos((0.5 * phi2));
	double tmp;
	if (lambda2 <= 4000000000000.0) {
		tmp = R * hypot(((t_1 - t_0) * lambda1), (phi1 - phi2));
	} else {
		tmp = R * hypot((lambda2 * (t_0 - t_1)), (phi1 - phi2));
	}
	return tmp;
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = Math.sin((0.5 * phi1)) * Math.sin((0.5 * phi2));
	double t_1 = Math.cos((0.5 * phi1)) * Math.cos((0.5 * phi2));
	double tmp;
	if (lambda2 <= 4000000000000.0) {
		tmp = R * Math.hypot(((t_1 - t_0) * lambda1), (phi1 - phi2));
	} else {
		tmp = R * Math.hypot((lambda2 * (t_0 - t_1)), (phi1 - phi2));
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = math.sin((0.5 * phi1)) * math.sin((0.5 * phi2))
	t_1 = math.cos((0.5 * phi1)) * math.cos((0.5 * phi2))
	tmp = 0
	if lambda2 <= 4000000000000.0:
		tmp = R * math.hypot(((t_1 - t_0) * lambda1), (phi1 - phi2))
	else:
		tmp = R * math.hypot((lambda2 * (t_0 - t_1)), (phi1 - phi2))
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(sin(Float64(0.5 * phi1)) * sin(Float64(0.5 * phi2)))
	t_1 = Float64(cos(Float64(0.5 * phi1)) * cos(Float64(0.5 * phi2)))
	tmp = 0.0
	if (lambda2 <= 4000000000000.0)
		tmp = Float64(R * hypot(Float64(Float64(t_1 - t_0) * lambda1), Float64(phi1 - phi2)));
	else
		tmp = Float64(R * hypot(Float64(lambda2 * Float64(t_0 - t_1)), Float64(phi1 - phi2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = sin((0.5 * phi1)) * sin((0.5 * phi2));
	t_1 = cos((0.5 * phi1)) * cos((0.5 * phi2));
	tmp = 0.0;
	if (lambda2 <= 4000000000000.0)
		tmp = R * hypot(((t_1 - t_0) * lambda1), (phi1 - phi2));
	else
		tmp = R * hypot((lambda2 * (t_0 - t_1)), (phi1 - phi2));
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(N[Sin[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[lambda2, 4000000000000.0], N[(R * N[Sqrt[N[(N[(t$95$1 - t$95$0), $MachinePrecision] * lambda1), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], N[(R * N[Sqrt[N[(lambda2 * N[(t$95$0 - t$95$1), $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 30.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(0.5 \cdot \phi_1\right) \cdot \left(R \cdot \left(\lambda_2 - \lambda_1\right)\right)\\ t_1 := R \cdot \left(\phi_2 - \phi_1\right)\\ \mathbf{if}\;\lambda_2 \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\lambda_2 \leq -5 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\lambda_2 \leq 600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\lambda_2 \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\lambda_2 \leq 2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left|\lambda_2 \cdot \left(R \cdot \cos \left(0.5 \cdot \left(\phi_1 + \phi_2\right)\right)\right)\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* (cos (* 0.5 phi1)) (* R (- lambda2 lambda1))))
        (t_1 (* R (- phi2 phi1))))
   (if (<= lambda2 -2.4e+24)
     t_1
     (if (<= lambda2 -5e-168)
       t_0
       (if (<= lambda2 600000000000.0)
         t_1
         (if (<= lambda2 2.2e+46)
           t_0
           (if (<= lambda2 2e+142)
             t_1
             (fabs (* lambda2 (* R (cos (* 0.5 (+ phi1 phi2)))))))))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	double t_1 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= -2.4e+24) {
		tmp = t_1;
	} else if (lambda2 <= -5e-168) {
		tmp = t_0;
	} else if (lambda2 <= 600000000000.0) {
		tmp = t_1;
	} else if (lambda2 <= 2.2e+46) {
		tmp = t_0;
	} else if (lambda2 <= 2e+142) {
		tmp = t_1;
	} else {
		tmp = fabs((lambda2 * (R * cos((0.5 * (phi1 + phi2))))));
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((0.5d0 * phi1)) * (r * (lambda2 - lambda1))
    t_1 = r * (phi2 - phi1)
    if (lambda2 <= (-2.4d+24)) then
        tmp = t_1
    else if (lambda2 <= (-5d-168)) then
        tmp = t_0
    else if (lambda2 <= 600000000000.0d0) then
        tmp = t_1
    else if (lambda2 <= 2.2d+46) then
        tmp = t_0
    else if (lambda2 <= 2d+142) then
        tmp = t_1
    else
        tmp = abs((lambda2 * (r * cos((0.5d0 * (phi1 + phi2))))))
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = Math.cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	double t_1 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= -2.4e+24) {
		tmp = t_1;
	} else if (lambda2 <= -5e-168) {
		tmp = t_0;
	} else if (lambda2 <= 600000000000.0) {
		tmp = t_1;
	} else if (lambda2 <= 2.2e+46) {
		tmp = t_0;
	} else if (lambda2 <= 2e+142) {
		tmp = t_1;
	} else {
		tmp = Math.abs((lambda2 * (R * Math.cos((0.5 * (phi1 + phi2))))));
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = math.cos((0.5 * phi1)) * (R * (lambda2 - lambda1))
	t_1 = R * (phi2 - phi1)
	tmp = 0
	if lambda2 <= -2.4e+24:
		tmp = t_1
	elif lambda2 <= -5e-168:
		tmp = t_0
	elif lambda2 <= 600000000000.0:
		tmp = t_1
	elif lambda2 <= 2.2e+46:
		tmp = t_0
	elif lambda2 <= 2e+142:
		tmp = t_1
	else:
		tmp = math.fabs((lambda2 * (R * math.cos((0.5 * (phi1 + phi2))))))
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(cos(Float64(0.5 * phi1)) * Float64(R * Float64(lambda2 - lambda1)))
	t_1 = Float64(R * Float64(phi2 - phi1))
	tmp = 0.0
	if (lambda2 <= -2.4e+24)
		tmp = t_1;
	elseif (lambda2 <= -5e-168)
		tmp = t_0;
	elseif (lambda2 <= 600000000000.0)
		tmp = t_1;
	elseif (lambda2 <= 2.2e+46)
		tmp = t_0;
	elseif (lambda2 <= 2e+142)
		tmp = t_1;
	else
		tmp = abs(Float64(lambda2 * Float64(R * cos(Float64(0.5 * Float64(phi1 + phi2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	t_1 = R * (phi2 - phi1);
	tmp = 0.0;
	if (lambda2 <= -2.4e+24)
		tmp = t_1;
	elseif (lambda2 <= -5e-168)
		tmp = t_0;
	elseif (lambda2 <= 600000000000.0)
		tmp = t_1;
	elseif (lambda2 <= 2.2e+46)
		tmp = t_0;
	elseif (lambda2 <= 2e+142)
		tmp = t_1;
	else
		tmp = abs((lambda2 * (R * cos((0.5 * (phi1 + phi2))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[(R * N[(lambda2 - lambda1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[lambda2, -2.4e+24], t$95$1, If[LessEqual[lambda2, -5e-168], t$95$0, If[LessEqual[lambda2, 600000000000.0], t$95$1, If[LessEqual[lambda2, 2.2e+46], t$95$0, If[LessEqual[lambda2, 2e+142], t$95$1, N[Abs[N[(lambda2 * N[(R * N[Cos[N[(0.5 * N[(phi1 + phi2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 87.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\lambda_2 \leq 2.6 \cdot 10^{+213}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\cos \left(0.5 \cdot \phi_1\right) \cdot \left(\lambda_1 - \lambda_2\right), \phi_1 - \phi_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left|\cos \left(0.5 \cdot \left(\phi_1 + \phi_2\right)\right) \cdot \left(R \cdot \lambda_2\right)\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (if (<= lambda2 2.6e+213)
   (* R (hypot (* (cos (* 0.5 phi1)) (- lambda1 lambda2)) (- phi1 phi2)))
   (fabs (* (cos (* 0.5 (+ phi1 phi2))) (* R lambda2)))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (lambda2 <= 2.6e+213) {
		tmp = R * hypot((cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	} else {
		tmp = fabs((cos((0.5 * (phi1 + phi2))) * (R * lambda2)));
	}
	return tmp;
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (lambda2 <= 2.6e+213) {
		tmp = R * Math.hypot((Math.cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	} else {
		tmp = Math.abs((Math.cos((0.5 * (phi1 + phi2))) * (R * lambda2)));
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	tmp = 0
	if lambda2 <= 2.6e+213:
		tmp = R * math.hypot((math.cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2))
	else:
		tmp = math.fabs((math.cos((0.5 * (phi1 + phi2))) * (R * lambda2)))
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0
	if (lambda2 <= 2.6e+213)
		tmp = Float64(R * hypot(Float64(cos(Float64(0.5 * phi1)) * Float64(lambda1 - lambda2)), Float64(phi1 - phi2)));
	else
		tmp = abs(Float64(cos(Float64(0.5 * Float64(phi1 + phi2))) * Float64(R * lambda2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0;
	if (lambda2 <= 2.6e+213)
		tmp = R * hypot((cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	else
		tmp = abs((cos((0.5 * (phi1 + phi2))) * (R * lambda2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := If[LessEqual[lambda2, 2.6e+213], N[(R * N[Sqrt[N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[(lambda1 - lambda2), $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], N[Abs[N[(N[Cos[N[(0.5 * N[(phi1 + phi2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(R * lambda2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 93.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\phi_1 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\cos \left(0.5 \cdot \phi_1\right) \cdot \left(\lambda_1 - \lambda_2\right), \phi_1 - \phi_2\right)\\ \mathbf{else}:\\ \;\;\;\;R \cdot \mathsf{hypot}\left(\cos \left(0.5 \cdot \phi_2\right) \cdot \left(\lambda_1 - \lambda_2\right), \phi_1 - \phi_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (if (<= phi1 -5e-8)
   (* R (hypot (* (cos (* 0.5 phi1)) (- lambda1 lambda2)) (- phi1 phi2)))
   (* R (hypot (* (cos (* 0.5 phi2)) (- lambda1 lambda2)) (- phi1 phi2)))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (phi1 <= -5e-8) {
		tmp = R * hypot((cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	} else {
		tmp = R * hypot((cos((0.5 * phi2)) * (lambda1 - lambda2)), (phi1 - phi2));
	}
	return tmp;
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (phi1 <= -5e-8) {
		tmp = R * Math.hypot((Math.cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	} else {
		tmp = R * Math.hypot((Math.cos((0.5 * phi2)) * (lambda1 - lambda2)), (phi1 - phi2));
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	tmp = 0
	if phi1 <= -5e-8:
		tmp = R * math.hypot((math.cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2))
	else:
		tmp = R * math.hypot((math.cos((0.5 * phi2)) * (lambda1 - lambda2)), (phi1 - phi2))
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0
	if (phi1 <= -5e-8)
		tmp = Float64(R * hypot(Float64(cos(Float64(0.5 * phi1)) * Float64(lambda1 - lambda2)), Float64(phi1 - phi2)));
	else
		tmp = Float64(R * hypot(Float64(cos(Float64(0.5 * phi2)) * Float64(lambda1 - lambda2)), Float64(phi1 - phi2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0;
	if (phi1 <= -5e-8)
		tmp = R * hypot((cos((0.5 * phi1)) * (lambda1 - lambda2)), (phi1 - phi2));
	else
		tmp = R * hypot((cos((0.5 * phi2)) * (lambda1 - lambda2)), (phi1 - phi2));
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := If[LessEqual[phi1, -5e-8], N[(R * N[Sqrt[N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[(lambda1 - lambda2), $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], N[(R * N[Sqrt[N[(N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision] * N[(lambda1 - lambda2), $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 96.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ R \cdot \mathsf{hypot}\left(\left(\lambda_1 - \lambda_2\right) \cdot \cos \left(\frac{\phi_1 + \phi_2}{2}\right), \phi_1 - \phi_2\right) \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (*
  R
  (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * hypot(((lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
}

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * Math.hypot(((lambda1 - lambda2) * Math.cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	return R * math.hypot(((lambda1 - lambda2) * math.cos(((phi1 + phi2) / 2.0))), (phi1 - phi2))

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	return Float64(R * hypot(Float64(Float64(lambda1 - lambda2) * cos(Float64(Float64(phi1 + phi2) / 2.0))), Float64(phi1 - phi2)))
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	tmp = R * hypot(((lambda1 - lambda2) * cos(((phi1 + phi2) / 2.0))), (phi1 - phi2));
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := N[(R * N[Sqrt[N[(N[(lambda1 - lambda2), $MachinePrecision] * N[Cos[N[(N[(phi1 + phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(phi1 - phi2), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 31.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(0.5 \cdot \phi_1\right)\\ t_1 := R \cdot \left(\phi_2 - \phi_1\right)\\ \mathbf{if}\;\lambda_2 \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\lambda_2 \leq -5 \cdot 10^{-168}:\\ \;\;\;\;R \cdot \left(t_0 \cdot \left(-\lambda_1\right)\right)\\ \mathbf{elif}\;\lambda_2 \leq 1.05 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\lambda_2 \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;\cos \left(0.5 \cdot \phi_2\right) \cdot \left(R \cdot \lambda_2\right)\\ \mathbf{elif}\;\lambda_2 \leq 1.22 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;R \cdot \left(t_0 \cdot \lambda_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (cos (* 0.5 phi1))) (t_1 (* R (- phi2 phi1))))
   (if (<= lambda2 -2.4e+24)
     t_1
     (if (<= lambda2 -5e-168)
       (* R (* t_0 (- lambda1)))
       (if (<= lambda2 1.05e+147)
         t_1
         (if (<= lambda2 2.25e+204)
           (* (cos (* 0.5 phi2)) (* R lambda2))
           (if (<= lambda2 1.22e+213) t_1 (* R (* t_0 lambda2)))))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = cos((0.5 * phi1));
	double t_1 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= -2.4e+24) {
		tmp = t_1;
	} else if (lambda2 <= -5e-168) {
		tmp = R * (t_0 * -lambda1);
	} else if (lambda2 <= 1.05e+147) {
		tmp = t_1;
	} else if (lambda2 <= 2.25e+204) {
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	} else if (lambda2 <= 1.22e+213) {
		tmp = t_1;
	} else {
		tmp = R * (t_0 * lambda2);
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((0.5d0 * phi1))
    t_1 = r * (phi2 - phi1)
    if (lambda2 <= (-2.4d+24)) then
        tmp = t_1
    else if (lambda2 <= (-5d-168)) then
        tmp = r * (t_0 * -lambda1)
    else if (lambda2 <= 1.05d+147) then
        tmp = t_1
    else if (lambda2 <= 2.25d+204) then
        tmp = cos((0.5d0 * phi2)) * (r * lambda2)
    else if (lambda2 <= 1.22d+213) then
        tmp = t_1
    else
        tmp = r * (t_0 * lambda2)
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = Math.cos((0.5 * phi1));
	double t_1 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= -2.4e+24) {
		tmp = t_1;
	} else if (lambda2 <= -5e-168) {
		tmp = R * (t_0 * -lambda1);
	} else if (lambda2 <= 1.05e+147) {
		tmp = t_1;
	} else if (lambda2 <= 2.25e+204) {
		tmp = Math.cos((0.5 * phi2)) * (R * lambda2);
	} else if (lambda2 <= 1.22e+213) {
		tmp = t_1;
	} else {
		tmp = R * (t_0 * lambda2);
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = math.cos((0.5 * phi1))
	t_1 = R * (phi2 - phi1)
	tmp = 0
	if lambda2 <= -2.4e+24:
		tmp = t_1
	elif lambda2 <= -5e-168:
		tmp = R * (t_0 * -lambda1)
	elif lambda2 <= 1.05e+147:
		tmp = t_1
	elif lambda2 <= 2.25e+204:
		tmp = math.cos((0.5 * phi2)) * (R * lambda2)
	elif lambda2 <= 1.22e+213:
		tmp = t_1
	else:
		tmp = R * (t_0 * lambda2)
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = cos(Float64(0.5 * phi1))
	t_1 = Float64(R * Float64(phi2 - phi1))
	tmp = 0.0
	if (lambda2 <= -2.4e+24)
		tmp = t_1;
	elseif (lambda2 <= -5e-168)
		tmp = Float64(R * Float64(t_0 * Float64(-lambda1)));
	elseif (lambda2 <= 1.05e+147)
		tmp = t_1;
	elseif (lambda2 <= 2.25e+204)
		tmp = Float64(cos(Float64(0.5 * phi2)) * Float64(R * lambda2));
	elseif (lambda2 <= 1.22e+213)
		tmp = t_1;
	else
		tmp = Float64(R * Float64(t_0 * lambda2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = cos((0.5 * phi1));
	t_1 = R * (phi2 - phi1);
	tmp = 0.0;
	if (lambda2 <= -2.4e+24)
		tmp = t_1;
	elseif (lambda2 <= -5e-168)
		tmp = R * (t_0 * -lambda1);
	elseif (lambda2 <= 1.05e+147)
		tmp = t_1;
	elseif (lambda2 <= 2.25e+204)
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	elseif (lambda2 <= 1.22e+213)
		tmp = t_1;
	else
		tmp = R * (t_0 * lambda2);
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[lambda2, -2.4e+24], t$95$1, If[LessEqual[lambda2, -5e-168], N[(R * N[(t$95$0 * (-lambda1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[lambda2, 1.05e+147], t$95$1, If[LessEqual[lambda2, 2.25e+204], N[(N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision] * N[(R * lambda2), $MachinePrecision]), $MachinePrecision], If[LessEqual[lambda2, 1.22e+213], t$95$1, N[(R * N[(t$95$0 * lambda2), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 33.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(0.5 \cdot \phi_1\right) \cdot \left(R \cdot \left(\lambda_2 - \lambda_1\right)\right)\\ t_1 := R \cdot \left(-\phi_1\right)\\ \mathbf{if}\;\phi_2 \leq -3.7 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\phi_2 \leq 8.8 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\phi_2 \leq 5.8 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\phi_2 \leq 3.9 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;R \cdot \left(\phi_2 - \phi_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* (cos (* 0.5 phi1)) (* R (- lambda2 lambda1))))
        (t_1 (* R (- phi1))))
   (if (<= phi2 -3.7e-192)
     t_1
     (if (<= phi2 8.8e-252)
       t_0
       (if (<= phi2 5.8e-217)
         t_1
         (if (<= phi2 3.9e+74) t_0 (* R (- phi2 phi1))))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	double t_1 = R * -phi1;
	double tmp;
	if (phi2 <= -3.7e-192) {
		tmp = t_1;
	} else if (phi2 <= 8.8e-252) {
		tmp = t_0;
	} else if (phi2 <= 5.8e-217) {
		tmp = t_1;
	} else if (phi2 <= 3.9e+74) {
		tmp = t_0;
	} else {
		tmp = R * (phi2 - phi1);
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((0.5d0 * phi1)) * (r * (lambda2 - lambda1))
    t_1 = r * -phi1
    if (phi2 <= (-3.7d-192)) then
        tmp = t_1
    else if (phi2 <= 8.8d-252) then
        tmp = t_0
    else if (phi2 <= 5.8d-217) then
        tmp = t_1
    else if (phi2 <= 3.9d+74) then
        tmp = t_0
    else
        tmp = r * (phi2 - phi1)
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = Math.cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	double t_1 = R * -phi1;
	double tmp;
	if (phi2 <= -3.7e-192) {
		tmp = t_1;
	} else if (phi2 <= 8.8e-252) {
		tmp = t_0;
	} else if (phi2 <= 5.8e-217) {
		tmp = t_1;
	} else if (phi2 <= 3.9e+74) {
		tmp = t_0;
	} else {
		tmp = R * (phi2 - phi1);
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = math.cos((0.5 * phi1)) * (R * (lambda2 - lambda1))
	t_1 = R * -phi1
	tmp = 0
	if phi2 <= -3.7e-192:
		tmp = t_1
	elif phi2 <= 8.8e-252:
		tmp = t_0
	elif phi2 <= 5.8e-217:
		tmp = t_1
	elif phi2 <= 3.9e+74:
		tmp = t_0
	else:
		tmp = R * (phi2 - phi1)
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(cos(Float64(0.5 * phi1)) * Float64(R * Float64(lambda2 - lambda1)))
	t_1 = Float64(R * Float64(-phi1))
	tmp = 0.0
	if (phi2 <= -3.7e-192)
		tmp = t_1;
	elseif (phi2 <= 8.8e-252)
		tmp = t_0;
	elseif (phi2 <= 5.8e-217)
		tmp = t_1;
	elseif (phi2 <= 3.9e+74)
		tmp = t_0;
	else
		tmp = Float64(R * Float64(phi2 - phi1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = cos((0.5 * phi1)) * (R * (lambda2 - lambda1));
	t_1 = R * -phi1;
	tmp = 0.0;
	if (phi2 <= -3.7e-192)
		tmp = t_1;
	elseif (phi2 <= 8.8e-252)
		tmp = t_0;
	elseif (phi2 <= 5.8e-217)
		tmp = t_1;
	elseif (phi2 <= 3.9e+74)
		tmp = t_0;
	else
		tmp = R * (phi2 - phi1);
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * N[(R * N[(lambda2 - lambda1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(R * (-phi1)), $MachinePrecision]}, If[LessEqual[phi2, -3.7e-192], t$95$1, If[LessEqual[phi2, 8.8e-252], t$95$0, If[LessEqual[phi2, 5.8e-217], t$95$1, If[LessEqual[phi2, 3.9e+74], t$95$0, N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 33.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := R \cdot \left(\lambda_2 - \lambda_1\right)\\ t_1 := R \cdot \left(-\phi_1\right)\\ \mathbf{if}\;\phi_2 \leq -5.8 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\phi_2 \leq 1.6 \cdot 10^{-254}:\\ \;\;\;\;\cos \left(0.5 \cdot \phi_2\right) \cdot t_0\\ \mathbf{elif}\;\phi_2 \leq 5.8 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\phi_2 \leq 3.9 \cdot 10^{+74}:\\ \;\;\;\;\cos \left(0.5 \cdot \phi_1\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;R \cdot \left(\phi_2 - \phi_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* R (- lambda2 lambda1))) (t_1 (* R (- phi1))))
   (if (<= phi2 -5.8e-47)
     t_1
     (if (<= phi2 1.6e-254)
       (* (cos (* 0.5 phi2)) t_0)
       (if (<= phi2 5.8e-217)
         t_1
         (if (<= phi2 3.9e+74)
           (* (cos (* 0.5 phi1)) t_0)
           (* R (- phi2 phi1))))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = R * (lambda2 - lambda1);
	double t_1 = R * -phi1;
	double tmp;
	if (phi2 <= -5.8e-47) {
		tmp = t_1;
	} else if (phi2 <= 1.6e-254) {
		tmp = cos((0.5 * phi2)) * t_0;
	} else if (phi2 <= 5.8e-217) {
		tmp = t_1;
	} else if (phi2 <= 3.9e+74) {
		tmp = cos((0.5 * phi1)) * t_0;
	} else {
		tmp = R * (phi2 - phi1);
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = r * (lambda2 - lambda1)
    t_1 = r * -phi1
    if (phi2 <= (-5.8d-47)) then
        tmp = t_1
    else if (phi2 <= 1.6d-254) then
        tmp = cos((0.5d0 * phi2)) * t_0
    else if (phi2 <= 5.8d-217) then
        tmp = t_1
    else if (phi2 <= 3.9d+74) then
        tmp = cos((0.5d0 * phi1)) * t_0
    else
        tmp = r * (phi2 - phi1)
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = R * (lambda2 - lambda1);
	double t_1 = R * -phi1;
	double tmp;
	if (phi2 <= -5.8e-47) {
		tmp = t_1;
	} else if (phi2 <= 1.6e-254) {
		tmp = Math.cos((0.5 * phi2)) * t_0;
	} else if (phi2 <= 5.8e-217) {
		tmp = t_1;
	} else if (phi2 <= 3.9e+74) {
		tmp = Math.cos((0.5 * phi1)) * t_0;
	} else {
		tmp = R * (phi2 - phi1);
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = R * (lambda2 - lambda1)
	t_1 = R * -phi1
	tmp = 0
	if phi2 <= -5.8e-47:
		tmp = t_1
	elif phi2 <= 1.6e-254:
		tmp = math.cos((0.5 * phi2)) * t_0
	elif phi2 <= 5.8e-217:
		tmp = t_1
	elif phi2 <= 3.9e+74:
		tmp = math.cos((0.5 * phi1)) * t_0
	else:
		tmp = R * (phi2 - phi1)
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(R * Float64(lambda2 - lambda1))
	t_1 = Float64(R * Float64(-phi1))
	tmp = 0.0
	if (phi2 <= -5.8e-47)
		tmp = t_1;
	elseif (phi2 <= 1.6e-254)
		tmp = Float64(cos(Float64(0.5 * phi2)) * t_0);
	elseif (phi2 <= 5.8e-217)
		tmp = t_1;
	elseif (phi2 <= 3.9e+74)
		tmp = Float64(cos(Float64(0.5 * phi1)) * t_0);
	else
		tmp = Float64(R * Float64(phi2 - phi1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = R * (lambda2 - lambda1);
	t_1 = R * -phi1;
	tmp = 0.0;
	if (phi2 <= -5.8e-47)
		tmp = t_1;
	elseif (phi2 <= 1.6e-254)
		tmp = cos((0.5 * phi2)) * t_0;
	elseif (phi2 <= 5.8e-217)
		tmp = t_1;
	elseif (phi2 <= 3.9e+74)
		tmp = cos((0.5 * phi1)) * t_0;
	else
		tmp = R * (phi2 - phi1);
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(R * N[(lambda2 - lambda1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(R * (-phi1)), $MachinePrecision]}, If[LessEqual[phi2, -5.8e-47], t$95$1, If[LessEqual[phi2, 1.6e-254], N[(N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[phi2, 5.8e-217], t$95$1, If[LessEqual[phi2, 3.9e+74], N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 34.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\lambda_2 \leq 9 \cdot 10^{+144} \lor \neg \left(\lambda_2 \leq 3.2 \cdot 10^{+204}\right) \land \lambda_2 \leq 3.2 \cdot 10^{+211}:\\ \;\;\;\;R \cdot \left(\phi_2 - \phi_1\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(0.5 \cdot \phi_2\right) \cdot \left(R \cdot \lambda_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (if (or (<= lambda2 9e+144)
         (and (not (<= lambda2 3.2e+204)) (<= lambda2 3.2e+211)))
   (* R (- phi2 phi1))
   (* (cos (* 0.5 phi2)) (* R lambda2))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if ((lambda2 <= 9e+144) || (!(lambda2 <= 3.2e+204) && (lambda2 <= 3.2e+211))) {
		tmp = R * (phi2 - phi1);
	} else {
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: tmp
    if ((lambda2 <= 9d+144) .or. (.not. (lambda2 <= 3.2d+204)) .and. (lambda2 <= 3.2d+211)) then
        tmp = r * (phi2 - phi1)
    else
        tmp = cos((0.5d0 * phi2)) * (r * lambda2)
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if ((lambda2 <= 9e+144) || (!(lambda2 <= 3.2e+204) && (lambda2 <= 3.2e+211))) {
		tmp = R * (phi2 - phi1);
	} else {
		tmp = Math.cos((0.5 * phi2)) * (R * lambda2);
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	tmp = 0
	if (lambda2 <= 9e+144) or (not (lambda2 <= 3.2e+204) and (lambda2 <= 3.2e+211)):
		tmp = R * (phi2 - phi1)
	else:
		tmp = math.cos((0.5 * phi2)) * (R * lambda2)
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0
	if ((lambda2 <= 9e+144) || (!(lambda2 <= 3.2e+204) && (lambda2 <= 3.2e+211)))
		tmp = Float64(R * Float64(phi2 - phi1));
	else
		tmp = Float64(cos(Float64(0.5 * phi2)) * Float64(R * lambda2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0;
	if ((lambda2 <= 9e+144) || (~((lambda2 <= 3.2e+204)) && (lambda2 <= 3.2e+211)))
		tmp = R * (phi2 - phi1);
	else
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := If[Or[LessEqual[lambda2, 9e+144], And[N[Not[LessEqual[lambda2, 3.2e+204]], $MachinePrecision], LessEqual[lambda2, 3.2e+211]]], N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision], N[(N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision] * N[(R * lambda2), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 34.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := R \cdot \left(\phi_2 - \phi_1\right)\\ \mathbf{if}\;\lambda_2 \leq 10^{+142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\lambda_2 \leq 5.6 \cdot 10^{+203}:\\ \;\;\;\;\cos \left(0.5 \cdot \phi_2\right) \cdot \left(R \cdot \lambda_2\right)\\ \mathbf{elif}\;\lambda_2 \leq 2.1 \cdot 10^{+213}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;R \cdot \left(\cos \left(0.5 \cdot \phi_1\right) \cdot \lambda_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (* R (- phi2 phi1))))
   (if (<= lambda2 1e+142)
     t_0
     (if (<= lambda2 5.6e+203)
       (* (cos (* 0.5 phi2)) (* R lambda2))
       (if (<= lambda2 2.1e+213) t_0 (* R (* (cos (* 0.5 phi1)) lambda2)))))))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= 1e+142) {
		tmp = t_0;
	} else if (lambda2 <= 5.6e+203) {
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	} else if (lambda2 <= 2.1e+213) {
		tmp = t_0;
	} else {
		tmp = R * (cos((0.5 * phi1)) * lambda2);
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = r * (phi2 - phi1)
    if (lambda2 <= 1d+142) then
        tmp = t_0
    else if (lambda2 <= 5.6d+203) then
        tmp = cos((0.5d0 * phi2)) * (r * lambda2)
    else if (lambda2 <= 2.1d+213) then
        tmp = t_0
    else
        tmp = r * (cos((0.5d0 * phi1)) * lambda2)
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = R * (phi2 - phi1);
	double tmp;
	if (lambda2 <= 1e+142) {
		tmp = t_0;
	} else if (lambda2 <= 5.6e+203) {
		tmp = Math.cos((0.5 * phi2)) * (R * lambda2);
	} else if (lambda2 <= 2.1e+213) {
		tmp = t_0;
	} else {
		tmp = R * (Math.cos((0.5 * phi1)) * lambda2);
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	t_0 = R * (phi2 - phi1)
	tmp = 0
	if lambda2 <= 1e+142:
		tmp = t_0
	elif lambda2 <= 5.6e+203:
		tmp = math.cos((0.5 * phi2)) * (R * lambda2)
	elif lambda2 <= 2.1e+213:
		tmp = t_0
	else:
		tmp = R * (math.cos((0.5 * phi1)) * lambda2)
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = Float64(R * Float64(phi2 - phi1))
	tmp = 0.0
	if (lambda2 <= 1e+142)
		tmp = t_0;
	elseif (lambda2 <= 5.6e+203)
		tmp = Float64(cos(Float64(0.5 * phi2)) * Float64(R * lambda2));
	elseif (lambda2 <= 2.1e+213)
		tmp = t_0;
	else
		tmp = Float64(R * Float64(cos(Float64(0.5 * phi1)) * lambda2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	t_0 = R * (phi2 - phi1);
	tmp = 0.0;
	if (lambda2 <= 1e+142)
		tmp = t_0;
	elseif (lambda2 <= 5.6e+203)
		tmp = cos((0.5 * phi2)) * (R * lambda2);
	elseif (lambda2 <= 2.1e+213)
		tmp = t_0;
	else
		tmp = R * (cos((0.5 * phi1)) * lambda2);
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[lambda2, 1e+142], t$95$0, If[LessEqual[lambda2, 5.6e+203], N[(N[Cos[N[(0.5 * phi2), $MachinePrecision]], $MachinePrecision] * N[(R * lambda2), $MachinePrecision]), $MachinePrecision], If[LessEqual[lambda2, 2.1e+213], t$95$0, N[(R * N[(N[Cos[N[(0.5 * phi1), $MachinePrecision]], $MachinePrecision] * lambda2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 29.1% accurate, 54.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\phi_1 \leq -2.22 \cdot 10^{-13}:\\ \;\;\;\;R \cdot \left(-\phi_1\right)\\ \mathbf{else}:\\ \;\;\;\;R \cdot \phi_2\\ \end{array} \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (if (<= phi1 -2.22e-13) (* R (- phi1)) (* R phi2)))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (phi1 <= -2.22e-13) {
		tmp = R * -phi1;
	} else {
		tmp = R * phi2;
	}
	return tmp;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8) :: tmp
    if (phi1 <= (-2.22d-13)) then
        tmp = r * -phi1
    else
        tmp = r * phi2
    end if
    code = tmp
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double tmp;
	if (phi1 <= -2.22e-13) {
		tmp = R * -phi1;
	} else {
		tmp = R * phi2;
	}
	return tmp;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	tmp = 0
	if phi1 <= -2.22e-13:
		tmp = R * -phi1
	else:
		tmp = R * phi2
	return tmp

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0
	if (phi1 <= -2.22e-13)
		tmp = Float64(R * Float64(-phi1));
	else
		tmp = Float64(R * phi2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(R, lambda1, lambda2, phi1, phi2)
	tmp = 0.0;
	if (phi1 <= -2.22e-13)
		tmp = R * -phi1;
	else
		tmp = R * phi2;
	end
	tmp_2 = tmp;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := If[LessEqual[phi1, -2.22e-13], N[(R * (-phi1)), $MachinePrecision], N[(R * phi2), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 30.5% accurate, 65.8× speedup

Math

\[\begin{array}{l} \\ R \cdot \left(\phi_2 - \phi_1\right) \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2) :precision binary64 (* R (- phi2 phi1)))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * (phi2 - phi1);
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    code = r * (phi2 - phi1)
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * (phi2 - phi1);
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	return R * (phi2 - phi1)

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	return Float64(R * Float64(phi2 - phi1))
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	tmp = R * (phi2 - phi1);
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := N[(R * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 18.0% accurate, 109.7× speedup

Math

\[\begin{array}{l} \\ R \cdot \phi_2 \end{array} \]

FPCore

(FPCore (R lambda1 lambda2 phi1 phi2) :precision binary64 (* R phi2))

C

double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * phi2;
}

Fortran

real(8) function code(r, lambda1, lambda2, phi1, phi2)
    real(8), intent (in) :: r
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: lambda2
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    code = r * phi2
end function

Java

public static double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * phi2;
}

Python

def code(R, lambda1, lambda2, phi1, phi2):
	return R * phi2

Julia

function code(R, lambda1, lambda2, phi1, phi2)
	return Float64(R * phi2)
end

MATLAB

function tmp = code(R, lambda1, lambda2, phi1, phi2)
	tmp = R * phi2;
end

Wolfram

code[R_, lambda1_, lambda2_, phi1_, phi2_] := N[(R * phi2), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024005 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Equirectangular approximation to distance on a great circle"
  :precision binary64
  (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))