Destination given bearing on a great circle

Percentage Accurate: 99.8% → 99.8%

Time: 19.2s

Alternatives: 13

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (* (sin theta) (sin delta)) (cos phi1))
   (-
    (cos delta)
    (*
     (sin phi1)
     (sin
      (asin
       (+
        (* (sin phi1) (cos delta))
        (* (* (cos phi1) (sin delta)) (cos theta))))))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2(((Math.sin(theta) * Math.sin(delta)) * Math.cos(phi1)), (Math.cos(delta) - (Math.sin(phi1) * Math.sin(Math.asin(((Math.sin(phi1) * Math.cos(delta)) + ((Math.cos(phi1) * Math.sin(delta)) * Math.cos(theta))))))));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2(((math.sin(theta) * math.sin(delta)) * math.cos(phi1)), (math.cos(delta) - (math.sin(phi1) * math.sin(math.asin(((math.sin(phi1) * math.cos(delta)) + ((math.cos(phi1) * math.sin(delta)) * math.cos(theta))))))))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(Float64(sin(theta) * sin(delta)) * cos(phi1)), Float64(cos(delta) - Float64(sin(phi1) * sin(asin(Float64(Float64(sin(phi1) * cos(delta)) + Float64(Float64(cos(phi1) * sin(delta)) * cos(theta)))))))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[(N[Sin[theta], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(N[Sin[phi1], $MachinePrecision] * N[Sin[N[ArcSin[N[(N[(N[Sin[phi1], $MachinePrecision] * N[Cos[delta], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Cos[phi1], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] * N[Cos[theta], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (* (sin theta) (sin delta)) (cos phi1))
   (-
    (cos delta)
    (*
     (sin phi1)
     (sin
      (asin
       (+
        (* (sin phi1) (cos delta))
        (* (* (cos phi1) (sin delta)) (cos theta))))))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2(((Math.sin(theta) * Math.sin(delta)) * Math.cos(phi1)), (Math.cos(delta) - (Math.sin(phi1) * Math.sin(Math.asin(((Math.sin(phi1) * Math.cos(delta)) + ((Math.cos(phi1) * Math.sin(delta)) * Math.cos(theta))))))));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2(((math.sin(theta) * math.sin(delta)) * math.cos(phi1)), (math.cos(delta) - (math.sin(phi1) * math.sin(math.asin(((math.sin(phi1) * math.cos(delta)) + ((math.cos(phi1) * math.sin(delta)) * math.cos(theta))))))))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(Float64(sin(theta) * sin(delta)) * cos(phi1)), Float64(cos(delta) - Float64(sin(phi1) * sin(asin(Float64(Float64(sin(phi1) * cos(delta)) + Float64(Float64(cos(phi1) * sin(delta)) * cos(theta)))))))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2(((sin(theta) * sin(delta)) * cos(phi1)), (cos(delta) - (sin(phi1) * sin(asin(((sin(phi1) * cos(delta)) + ((cos(phi1) * sin(delta)) * cos(theta))))))));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[(N[Sin[theta], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(N[Sin[phi1], $MachinePrecision] * N[Sin[N[ArcSin[N[(N[(N[Sin[phi1], $MachinePrecision] * N[Cos[delta], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Cos[phi1], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] * N[Cos[theta], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)}{\cos delta - \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \phi_1 \cdot \mathsf{fma}\left(\cos delta, \sin \phi_1, \cos \phi_1 \cdot \left(\sin delta \cdot \cos theta\right)\right)\right)\right)} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (sin theta) (* (sin delta) (cos phi1)))
   (-
    (cos delta)
    (expm1
     (log1p
      (*
       (sin phi1)
       (fma
        (cos delta)
        (sin phi1)
        (* (cos phi1) (* (sin delta) (cos theta)))))))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - expm1(log1p((sin(phi1) * fma(cos(delta), sin(phi1), (cos(phi1) * (sin(delta) * cos(theta)))))))));
}

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * Float64(sin(delta) * cos(phi1))), Float64(cos(delta) - expm1(log1p(Float64(sin(phi1) * fma(cos(delta), sin(phi1), Float64(cos(phi1) * Float64(sin(delta) * cos(theta))))))))))
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(Exp[N[Log[1 + N[(N[Sin[phi1], $MachinePrecision] * N[(N[Cos[delta], $MachinePrecision] * N[Sin[phi1], $MachinePrecision] + N[(N[Cos[phi1], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[theta], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)}{\cos delta - \left(\sin \phi_1 \cdot \left(\cos \phi_1 \cdot \left(\sin delta \cdot \cos theta\right)\right) + \cos delta \cdot {\sin \phi_1}^{2}\right)} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (sin theta) (* (sin delta) (cos phi1)))
   (-
    (cos delta)
    (+
     (* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta))))
     (* (cos delta) (pow (sin phi1) 2.0)))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - ((sin(phi1) * (cos(phi1) * (sin(delta) * cos(theta)))) + (cos(delta) * pow(sin(phi1), 2.0)))));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - ((sin(phi1) * (cos(phi1) * (sin(delta) * cos(theta)))) + (cos(delta) * (sin(phi1) ** 2.0d0)))))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((Math.sin(theta) * (Math.sin(delta) * Math.cos(phi1))), (Math.cos(delta) - ((Math.sin(phi1) * (Math.cos(phi1) * (Math.sin(delta) * Math.cos(theta)))) + (Math.cos(delta) * Math.pow(Math.sin(phi1), 2.0)))));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((math.sin(theta) * (math.sin(delta) * math.cos(phi1))), (math.cos(delta) - ((math.sin(phi1) * (math.cos(phi1) * (math.sin(delta) * math.cos(theta)))) + (math.cos(delta) * math.pow(math.sin(phi1), 2.0)))))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * Float64(sin(delta) * cos(phi1))), Float64(cos(delta) - Float64(Float64(sin(phi1) * Float64(cos(phi1) * Float64(sin(delta) * cos(theta)))) + Float64(cos(delta) * (sin(phi1) ^ 2.0))))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - ((sin(phi1) * (cos(phi1) * (sin(delta) * cos(theta)))) + (cos(delta) * (sin(phi1) ^ 2.0)))));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(N[(N[Sin[phi1], $MachinePrecision] * N[(N[Cos[phi1], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[theta], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[delta], $MachinePrecision] * N[Power[N[Sin[phi1], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)}{\cos delta - \sin \phi_1 \cdot \left(\cos \phi_1 \cdot \left(\sin delta \cdot \cos theta\right) + \cos delta \cdot \sin \phi_1\right)} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (sin theta) (* (sin delta) (cos phi1)))
   (-
    (cos delta)
    (*
     (sin phi1)
     (+
      (* (cos phi1) (* (sin delta) (cos theta)))
      (* (cos delta) (sin phi1))))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - (sin(phi1) * ((cos(phi1) * (sin(delta) * cos(theta))) + (cos(delta) * sin(phi1))))));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - (sin(phi1) * ((cos(phi1) * (sin(delta) * cos(theta))) + (cos(delta) * sin(phi1))))))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((Math.sin(theta) * (Math.sin(delta) * Math.cos(phi1))), (Math.cos(delta) - (Math.sin(phi1) * ((Math.cos(phi1) * (Math.sin(delta) * Math.cos(theta))) + (Math.cos(delta) * Math.sin(phi1))))));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((math.sin(theta) * (math.sin(delta) * math.cos(phi1))), (math.cos(delta) - (math.sin(phi1) * ((math.cos(phi1) * (math.sin(delta) * math.cos(theta))) + (math.cos(delta) * math.sin(phi1))))))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * Float64(sin(delta) * cos(phi1))), Float64(cos(delta) - Float64(sin(phi1) * Float64(Float64(cos(phi1) * Float64(sin(delta) * cos(theta))) + Float64(cos(delta) * sin(phi1)))))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - (sin(phi1) * ((cos(phi1) * (sin(delta) * cos(theta))) + (cos(delta) * sin(phi1))))));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(N[Sin[phi1], $MachinePrecision] * N[(N[(N[Cos[phi1], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[theta], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[delta], $MachinePrecision] * N[Sin[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 94.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin delta \cdot \cos \phi_1\\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot t_1}{\cos delta - \sin \phi_1 \cdot \left(\cos delta \cdot \sin \phi_1 + t_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (let* ((t_1 (* (sin delta) (cos phi1))))
   (+
    lambda1
    (atan2
     (* (sin theta) t_1)
     (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) t_1)))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = sin(delta) * cos(phi1);
	return lambda1 + atan2((sin(theta) * t_1), (cos(delta) - (sin(phi1) * ((cos(delta) * sin(phi1)) + t_1))));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    real(8) :: t_1
    t_1 = sin(delta) * cos(phi1)
    code = lambda1 + atan2((sin(theta) * t_1), (cos(delta) - (sin(phi1) * ((cos(delta) * sin(phi1)) + t_1))))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = Math.sin(delta) * Math.cos(phi1);
	return lambda1 + Math.atan2((Math.sin(theta) * t_1), (Math.cos(delta) - (Math.sin(phi1) * ((Math.cos(delta) * Math.sin(phi1)) + t_1))));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	t_1 = math.sin(delta) * math.cos(phi1)
	return lambda1 + math.atan2((math.sin(theta) * t_1), (math.cos(delta) - (math.sin(phi1) * ((math.cos(delta) * math.sin(phi1)) + t_1))))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	t_1 = Float64(sin(delta) * cos(phi1))
	return Float64(lambda1 + atan(Float64(sin(theta) * t_1), Float64(cos(delta) - Float64(sin(phi1) * Float64(Float64(cos(delta) * sin(phi1)) + t_1)))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	t_1 = sin(delta) * cos(phi1);
	tmp = lambda1 + atan2((sin(theta) * t_1), (cos(delta) - (sin(phi1) * ((cos(delta) * sin(phi1)) + t_1))));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := Block[{t$95$1 = N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]}, N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * t$95$1), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[(N[Sin[phi1], $MachinePrecision] * N[(N[(N[Cos[delta], $MachinePrecision] * N[Sin[phi1], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 91.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin delta \cdot \cos \phi_1\\ t_2 := \sin theta \cdot t_1\\ \mathbf{if}\;delta \leq -1.05 \cdot 10^{-6}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{t_2}{\cos delta}\\ \mathbf{elif}\;delta \leq 6.2 \cdot 10^{+27}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{t_2}{{\cos \phi_1}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(t_1\right)\right)}{\cos delta}\\ \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (let* ((t_1 (* (sin delta) (cos phi1))) (t_2 (* (sin theta) t_1)))
   (if (<= delta -1.05e-6)
     (+ lambda1 (atan2 t_2 (cos delta)))
     (if (<= delta 6.2e+27)
       (+ lambda1 (atan2 t_2 (pow (cos phi1) 2.0)))
       (+ lambda1 (atan2 (* (sin theta) (log1p (expm1 t_1))) (cos delta)))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = sin(delta) * cos(phi1);
	double t_2 = sin(theta) * t_1;
	double tmp;
	if (delta <= -1.05e-6) {
		tmp = lambda1 + atan2(t_2, cos(delta));
	} else if (delta <= 6.2e+27) {
		tmp = lambda1 + atan2(t_2, pow(cos(phi1), 2.0));
	} else {
		tmp = lambda1 + atan2((sin(theta) * log1p(expm1(t_1))), cos(delta));
	}
	return tmp;
}

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = Math.sin(delta) * Math.cos(phi1);
	double t_2 = Math.sin(theta) * t_1;
	double tmp;
	if (delta <= -1.05e-6) {
		tmp = lambda1 + Math.atan2(t_2, Math.cos(delta));
	} else if (delta <= 6.2e+27) {
		tmp = lambda1 + Math.atan2(t_2, Math.pow(Math.cos(phi1), 2.0));
	} else {
		tmp = lambda1 + Math.atan2((Math.sin(theta) * Math.log1p(Math.expm1(t_1))), Math.cos(delta));
	}
	return tmp;
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	t_1 = math.sin(delta) * math.cos(phi1)
	t_2 = math.sin(theta) * t_1
	tmp = 0
	if delta <= -1.05e-6:
		tmp = lambda1 + math.atan2(t_2, math.cos(delta))
	elif delta <= 6.2e+27:
		tmp = lambda1 + math.atan2(t_2, math.pow(math.cos(phi1), 2.0))
	else:
		tmp = lambda1 + math.atan2((math.sin(theta) * math.log1p(math.expm1(t_1))), math.cos(delta))
	return tmp

Julia

function code(lambda1, phi1, phi2, delta, theta)
	t_1 = Float64(sin(delta) * cos(phi1))
	t_2 = Float64(sin(theta) * t_1)
	tmp = 0.0
	if (delta <= -1.05e-6)
		tmp = Float64(lambda1 + atan(t_2, cos(delta)));
	elseif (delta <= 6.2e+27)
		tmp = Float64(lambda1 + atan(t_2, (cos(phi1) ^ 2.0)));
	else
		tmp = Float64(lambda1 + atan(Float64(sin(theta) * log1p(expm1(t_1))), cos(delta)));
	end
	return tmp
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := Block[{t$95$1 = N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sin[theta], $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[delta, -1.05e-6], N[(lambda1 + N[ArcTan[t$95$2 / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[delta, 6.2e+27], N[(lambda1 + N[ArcTan[t$95$2 / N[Power[N[Cos[phi1], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[Log[1 + N[(Exp[t$95$1] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 92.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)}{\cos delta - {\sin \phi_1}^{2}} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+
  lambda1
  (atan2
   (* (sin theta) (* (sin delta) (cos phi1)))
   (- (cos delta) (pow (sin phi1) 2.0)))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - pow(sin(phi1), 2.0)));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - (sin(phi1) ** 2.0d0)))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((Math.sin(theta) * (Math.sin(delta) * Math.cos(phi1))), (Math.cos(delta) - Math.pow(Math.sin(phi1), 2.0)));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((math.sin(theta) * (math.sin(delta) * math.cos(phi1))), (math.cos(delta) - math.pow(math.sin(phi1), 2.0)))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * Float64(sin(delta) * cos(phi1))), Float64(cos(delta) - (sin(phi1) ^ 2.0))))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), (cos(delta) - (sin(phi1) ^ 2.0)));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[delta], $MachinePrecision] - N[Power[N[Sin[phi1], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 7: 91.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)\\ \mathbf{if}\;delta \leq -3 \cdot 10^{-6} \lor \neg \left(delta \leq 6.2 \cdot 10^{+27}\right):\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{t_1}{\cos delta}\\ \mathbf{else}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{t_1}{{\cos \phi_1}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (let* ((t_1 (* (sin theta) (* (sin delta) (cos phi1)))))
   (if (or (<= delta -3e-6) (not (<= delta 6.2e+27)))
     (+ lambda1 (atan2 t_1 (cos delta)))
     (+ lambda1 (atan2 t_1 (pow (cos phi1) 2.0))))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = sin(theta) * (sin(delta) * cos(phi1));
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 6.2e+27)) {
		tmp = lambda1 + atan2(t_1, cos(delta));
	} else {
		tmp = lambda1 + atan2(t_1, pow(cos(phi1), 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sin(theta) * (sin(delta) * cos(phi1))
    if ((delta <= (-3d-6)) .or. (.not. (delta <= 6.2d+27))) then
        tmp = lambda1 + atan2(t_1, cos(delta))
    else
        tmp = lambda1 + atan2(t_1, (cos(phi1) ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double t_1 = Math.sin(theta) * (Math.sin(delta) * Math.cos(phi1));
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 6.2e+27)) {
		tmp = lambda1 + Math.atan2(t_1, Math.cos(delta));
	} else {
		tmp = lambda1 + Math.atan2(t_1, Math.pow(Math.cos(phi1), 2.0));
	}
	return tmp;
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	t_1 = math.sin(theta) * (math.sin(delta) * math.cos(phi1))
	tmp = 0
	if (delta <= -3e-6) or not (delta <= 6.2e+27):
		tmp = lambda1 + math.atan2(t_1, math.cos(delta))
	else:
		tmp = lambda1 + math.atan2(t_1, math.pow(math.cos(phi1), 2.0))
	return tmp

Julia

function code(lambda1, phi1, phi2, delta, theta)
	t_1 = Float64(sin(theta) * Float64(sin(delta) * cos(phi1)))
	tmp = 0.0
	if ((delta <= -3e-6) || !(delta <= 6.2e+27))
		tmp = Float64(lambda1 + atan(t_1, cos(delta)));
	else
		tmp = Float64(lambda1 + atan(t_1, (cos(phi1) ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(lambda1, phi1, phi2, delta, theta)
	t_1 = sin(theta) * (sin(delta) * cos(phi1));
	tmp = 0.0;
	if ((delta <= -3e-6) || ~((delta <= 6.2e+27)))
		tmp = lambda1 + atan2(t_1, cos(delta));
	else
		tmp = lambda1 + atan2(t_1, (cos(phi1) ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := Block[{t$95$1 = N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[delta, -3e-6], N[Not[LessEqual[delta, 6.2e+27]], $MachinePrecision]], N[(lambda1 + N[ArcTan[t$95$1 / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(lambda1 + N[ArcTan[t$95$1 / N[Power[N[Cos[phi1], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 91.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;delta \leq -3 \cdot 10^{-6} \lor \neg \left(delta \leq 0.00094\right):\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \left(\sin delta \cdot \cos \phi_1\right)}{\cos delta}\\ \mathbf{else}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\cos \phi_1 \cdot \left(\sin theta \cdot delta\right)}{\frac{1 + \cos \left(\phi_1 \cdot 2\right)}{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (if (or (<= delta -3e-6) (not (<= delta 0.00094)))
   (+ lambda1 (atan2 (* (sin theta) (* (sin delta) (cos phi1))) (cos delta)))
   (+
    lambda1
    (atan2
     (* (cos phi1) (* (sin theta) delta))
     (/ (+ 1.0 (cos (* phi1 2.0))) 2.0)))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 0.00094)) {
		tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), cos(delta));
	} else {
		tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0 + cos((phi1 * 2.0))) / 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    real(8) :: tmp
    if ((delta <= (-3d-6)) .or. (.not. (delta <= 0.00094d0))) then
        tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), cos(delta))
    else
        tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0d0 + cos((phi1 * 2.0d0))) / 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 0.00094)) {
		tmp = lambda1 + Math.atan2((Math.sin(theta) * (Math.sin(delta) * Math.cos(phi1))), Math.cos(delta));
	} else {
		tmp = lambda1 + Math.atan2((Math.cos(phi1) * (Math.sin(theta) * delta)), ((1.0 + Math.cos((phi1 * 2.0))) / 2.0));
	}
	return tmp;
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	tmp = 0
	if (delta <= -3e-6) or not (delta <= 0.00094):
		tmp = lambda1 + math.atan2((math.sin(theta) * (math.sin(delta) * math.cos(phi1))), math.cos(delta))
	else:
		tmp = lambda1 + math.atan2((math.cos(phi1) * (math.sin(theta) * delta)), ((1.0 + math.cos((phi1 * 2.0))) / 2.0))
	return tmp

Julia

function code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0
	if ((delta <= -3e-6) || !(delta <= 0.00094))
		tmp = Float64(lambda1 + atan(Float64(sin(theta) * Float64(sin(delta) * cos(phi1))), cos(delta)));
	else
		tmp = Float64(lambda1 + atan(Float64(cos(phi1) * Float64(sin(theta) * delta)), Float64(Float64(1.0 + cos(Float64(phi1 * 2.0))) / 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0;
	if ((delta <= -3e-6) || ~((delta <= 0.00094)))
		tmp = lambda1 + atan2((sin(theta) * (sin(delta) * cos(phi1))), cos(delta));
	else
		tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0 + cos((phi1 * 2.0))) / 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := If[Or[LessEqual[delta, -3e-6], N[Not[LessEqual[delta, 0.00094]], $MachinePrecision]], N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[(N[Sin[delta], $MachinePrecision] * N[Cos[phi1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(lambda1 + N[ArcTan[N[(N[Cos[phi1], $MachinePrecision] * N[(N[Sin[theta], $MachinePrecision] * delta), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + N[Cos[N[(phi1 * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 89.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;delta \leq -3 \cdot 10^{-6} \lor \neg \left(delta \leq 0.0042\right):\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \sin delta}{\cos delta}\\ \mathbf{else}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\cos \phi_1 \cdot \left(\sin theta \cdot delta\right)}{\frac{1 + \cos \left(\phi_1 \cdot 2\right)}{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (if (or (<= delta -3e-6) (not (<= delta 0.0042)))
   (+ lambda1 (atan2 (* (sin theta) (sin delta)) (cos delta)))
   (+
    lambda1
    (atan2
     (* (cos phi1) (* (sin theta) delta))
     (/ (+ 1.0 (cos (* phi1 2.0))) 2.0)))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 0.0042)) {
		tmp = lambda1 + atan2((sin(theta) * sin(delta)), cos(delta));
	} else {
		tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0 + cos((phi1 * 2.0))) / 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    real(8) :: tmp
    if ((delta <= (-3d-6)) .or. (.not. (delta <= 0.0042d0))) then
        tmp = lambda1 + atan2((sin(theta) * sin(delta)), cos(delta))
    else
        tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0d0 + cos((phi1 * 2.0d0))) / 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if ((delta <= -3e-6) || !(delta <= 0.0042)) {
		tmp = lambda1 + Math.atan2((Math.sin(theta) * Math.sin(delta)), Math.cos(delta));
	} else {
		tmp = lambda1 + Math.atan2((Math.cos(phi1) * (Math.sin(theta) * delta)), ((1.0 + Math.cos((phi1 * 2.0))) / 2.0));
	}
	return tmp;
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	tmp = 0
	if (delta <= -3e-6) or not (delta <= 0.0042):
		tmp = lambda1 + math.atan2((math.sin(theta) * math.sin(delta)), math.cos(delta))
	else:
		tmp = lambda1 + math.atan2((math.cos(phi1) * (math.sin(theta) * delta)), ((1.0 + math.cos((phi1 * 2.0))) / 2.0))
	return tmp

Julia

function code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0
	if ((delta <= -3e-6) || !(delta <= 0.0042))
		tmp = Float64(lambda1 + atan(Float64(sin(theta) * sin(delta)), cos(delta)));
	else
		tmp = Float64(lambda1 + atan(Float64(cos(phi1) * Float64(sin(theta) * delta)), Float64(Float64(1.0 + cos(Float64(phi1 * 2.0))) / 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0;
	if ((delta <= -3e-6) || ~((delta <= 0.0042)))
		tmp = lambda1 + atan2((sin(theta) * sin(delta)), cos(delta));
	else
		tmp = lambda1 + atan2((cos(phi1) * (sin(theta) * delta)), ((1.0 + cos((phi1 * 2.0))) / 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := If[Or[LessEqual[delta, -3e-6], N[Not[LessEqual[delta, 0.0042]], $MachinePrecision]], N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(lambda1 + N[ArcTan[N[(N[Cos[phi1], $MachinePrecision] * N[(N[Sin[theta], $MachinePrecision] * delta), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + N[Cos[N[(phi1 * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 86.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot \sin delta}{\cos delta} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+ lambda1 (atan2 (* (sin theta) (sin delta)) (cos delta))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * sin(delta)), cos(delta));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((sin(theta) * sin(delta)), cos(delta))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((Math.sin(theta) * Math.sin(delta)), Math.cos(delta));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((math.sin(theta) * math.sin(delta)), math.cos(delta))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * sin(delta)), cos(delta)))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((sin(theta) * sin(delta)), cos(delta));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * N[Sin[delta], $MachinePrecision]), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 77.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;delta \leq -5.4 \cdot 10^{+56}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{theta \cdot \sin delta}{\cos delta}\\ \mathbf{else}:\\ \;\;\;\;\lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot delta}{\cos delta}\\ \end{array} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (if (<= delta -5.4e+56)
   (+ lambda1 (atan2 (* theta (sin delta)) (cos delta)))
   (+ lambda1 (atan2 (* (sin theta) delta) (cos delta)))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if (delta <= -5.4e+56) {
		tmp = lambda1 + atan2((theta * sin(delta)), cos(delta));
	} else {
		tmp = lambda1 + atan2((sin(theta) * delta), cos(delta));
	}
	return tmp;
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    real(8) :: tmp
    if (delta <= (-5.4d+56)) then
        tmp = lambda1 + atan2((theta * sin(delta)), cos(delta))
    else
        tmp = lambda1 + atan2((sin(theta) * delta), cos(delta))
    end if
    code = tmp
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	double tmp;
	if (delta <= -5.4e+56) {
		tmp = lambda1 + Math.atan2((theta * Math.sin(delta)), Math.cos(delta));
	} else {
		tmp = lambda1 + Math.atan2((Math.sin(theta) * delta), Math.cos(delta));
	}
	return tmp;
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	tmp = 0
	if delta <= -5.4e+56:
		tmp = lambda1 + math.atan2((theta * math.sin(delta)), math.cos(delta))
	else:
		tmp = lambda1 + math.atan2((math.sin(theta) * delta), math.cos(delta))
	return tmp

Julia

function code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0
	if (delta <= -5.4e+56)
		tmp = Float64(lambda1 + atan(Float64(theta * sin(delta)), cos(delta)));
	else
		tmp = Float64(lambda1 + atan(Float64(sin(theta) * delta), cos(delta)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(lambda1, phi1, phi2, delta, theta)
	tmp = 0.0;
	if (delta <= -5.4e+56)
		tmp = lambda1 + atan2((theta * sin(delta)), cos(delta));
	else
		tmp = lambda1 + atan2((sin(theta) * delta), cos(delta));
	end
	tmp_2 = tmp;
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := If[LessEqual[delta, -5.4e+56], N[(lambda1 + N[ArcTan[N[(theta * N[Sin[delta], $MachinePrecision]), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * delta), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 74.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{\sin theta \cdot delta}{\cos delta} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+ lambda1 (atan2 (* (sin theta) delta) (cos delta))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((sin(theta) * delta), cos(delta));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((sin(theta) * delta), cos(delta))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((Math.sin(theta) * delta), Math.cos(delta));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((math.sin(theta) * delta), math.cos(delta))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(sin(theta) * delta), cos(delta)))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((sin(theta) * delta), cos(delta));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(N[Sin[theta], $MachinePrecision] * delta), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 67.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \lambda_1 + \tan^{-1}_* \frac{theta \cdot delta}{\cos delta} \end{array} \]

FPCore

(FPCore (lambda1 phi1 phi2 delta theta)
 :precision binary64
 (+ lambda1 (atan2 (* theta delta) (cos delta))))

C

double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + atan2((theta * delta), cos(delta));
}

Fortran

real(8) function code(lambda1, phi1, phi2, delta, theta)
    real(8), intent (in) :: lambda1
    real(8), intent (in) :: phi1
    real(8), intent (in) :: phi2
    real(8), intent (in) :: delta
    real(8), intent (in) :: theta
    code = lambda1 + atan2((theta * delta), cos(delta))
end function

Java

public static double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return lambda1 + Math.atan2((theta * delta), Math.cos(delta));
}

Python

def code(lambda1, phi1, phi2, delta, theta):
	return lambda1 + math.atan2((theta * delta), math.cos(delta))

Julia

function code(lambda1, phi1, phi2, delta, theta)
	return Float64(lambda1 + atan(Float64(theta * delta), cos(delta)))
end

MATLAB

function tmp = code(lambda1, phi1, phi2, delta, theta)
	tmp = lambda1 + atan2((theta * delta), cos(delta));
end

Wolfram

code[lambda1_, phi1_, phi2_, delta_, theta_] := N[(lambda1 + N[ArcTan[N[(theta * delta), $MachinePrecision] / N[Cos[delta], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023342 
(FPCore (lambda1 phi1 phi2 delta theta)
  :name "Destination given bearing on a great circle"
  :precision binary64
  (+ lambda1 (atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))