Average Error: 24.0 → 23.4
Time: 50.1s
Precision: binary64
\[R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{{\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)}}{\sqrt{1 - \left({\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right)}}\right) \]
↓
\[\begin{array}{l} t_0 := {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\\ t_1 := \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\\ t_2 := \mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_1\right)\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\\ t_3 := \mathsf{fma}\left(\cos \phi_2 \cdot 0.5, \cos \phi_1, t_0\right)\\ R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(t_1 \cdot t_1\right), t_0\right)}}{\sqrt{\sqrt{{\left(\frac{{t_2}^{3} - {t_3}^{3}}{{t_2}^{2} + \left({t_3}^{2} + t_2 \cdot t_3\right)}\right)}^{2}}}}\right) \end{array} \]
(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (*
  R
  (*
   2.0
   (atan2
    (sqrt
     (+
      (pow (sin (/ (- phi1 phi2) 2.0)) 2.0)
      (*
       (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2.0)))
       (sin (/ (- lambda1 lambda2) 2.0)))))
    (sqrt
     (-
      1.0
      (+
       (pow (sin (/ (- phi1 phi2) 2.0)) 2.0)
       (*
        (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2.0)))
        (sin (/ (- lambda1 lambda2) 2.0))))))))))
↓
(FPCore (R lambda1 lambda2 phi1 phi2)
 :precision binary64
 (let* ((t_0 (pow (sin (* -0.5 (- phi2 phi1))) 2.0))
        (t_1 (sin (/ (- lambda2 lambda1) 2.0)))
        (t_2
         (fma
          0.5
          (* (cos lambda2) (* (cos phi1) (* (cos phi2) (cos lambda1))))
          (fma
           0.5
           (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
           1.0)))
        (t_3 (fma (* (cos phi2) 0.5) (cos phi1) t_0)))
   (*
    R
    (*
     2.0
     (atan2
      (sqrt (fma (cos phi1) (* (cos phi2) (* t_1 t_1)) t_0))
      (sqrt
       (sqrt
        (pow
         (/
          (- (pow t_2 3.0) (pow t_3 3.0))
          (+ (pow t_2 2.0) (+ (pow t_3 2.0) (* t_2 t_3))))
         2.0))))))))
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return R * (2.0 * atan2(sqrt((pow(sin(((phi1 - phi2) / 2.0)), 2.0) + (((cos(phi1) * cos(phi2)) * sin(((lambda1 - lambda2) / 2.0))) * sin(((lambda1 - lambda2) / 2.0))))), sqrt((1.0 - (pow(sin(((phi1 - phi2) / 2.0)), 2.0) + (((cos(phi1) * cos(phi2)) * sin(((lambda1 - lambda2) / 2.0))) * sin(((lambda1 - lambda2) / 2.0))))))));
}
↓
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double t_0 = pow(sin((-0.5 * (phi2 - phi1))), 2.0);
	double t_1 = sin(((lambda2 - lambda1) / 2.0));
	double t_2 = fma(0.5, (cos(lambda2) * (cos(phi1) * (cos(phi2) * cos(lambda1)))), fma(0.5, (cos(phi1) * (cos(phi2) * (sin(lambda1) * sin(lambda2)))), 1.0));
	double t_3 = fma((cos(phi2) * 0.5), cos(phi1), t_0);
	return R * (2.0 * atan2(sqrt(fma(cos(phi1), (cos(phi2) * (t_1 * t_1)), t_0)), sqrt(sqrt(pow(((pow(t_2, 3.0) - pow(t_3, 3.0)) / (pow(t_2, 2.0) + (pow(t_3, 2.0) + (t_2 * t_3)))), 2.0)))));
}

function code(R, lambda1, lambda2, phi1, phi2)
	return Float64(R * Float64(2.0 * atan(sqrt(Float64((sin(Float64(Float64(phi1 - phi2) / 2.0)) ^ 2.0) + Float64(Float64(Float64(cos(phi1) * cos(phi2)) * sin(Float64(Float64(lambda1 - lambda2) / 2.0))) * sin(Float64(Float64(lambda1 - lambda2) / 2.0))))), sqrt(Float64(1.0 - Float64((sin(Float64(Float64(phi1 - phi2) / 2.0)) ^ 2.0) + Float64(Float64(Float64(cos(phi1) * cos(phi2)) * sin(Float64(Float64(lambda1 - lambda2) / 2.0))) * sin(Float64(Float64(lambda1 - lambda2) / 2.0)))))))))
end
↓
function code(R, lambda1, lambda2, phi1, phi2)
	t_0 = sin(Float64(-0.5 * Float64(phi2 - phi1))) ^ 2.0
	t_1 = sin(Float64(Float64(lambda2 - lambda1) / 2.0))
	t_2 = fma(0.5, Float64(cos(lambda2) * Float64(cos(phi1) * Float64(cos(phi2) * cos(lambda1)))), fma(0.5, Float64(cos(phi1) * Float64(cos(phi2) * Float64(sin(lambda1) * sin(lambda2)))), 1.0))
	t_3 = fma(Float64(cos(phi2) * 0.5), cos(phi1), t_0)
	return Float64(R * Float64(2.0 * atan(sqrt(fma(cos(phi1), Float64(cos(phi2) * Float64(t_1 * t_1)), t_0)), sqrt(sqrt((Float64(Float64((t_2 ^ 3.0) - (t_3 ^ 3.0)) / Float64((t_2 ^ 2.0) + Float64((t_3 ^ 2.0) + Float64(t_2 * t_3)))) ^ 2.0))))))
end

code[R_, lambda1_, lambda2_, phi1_, phi2_] := N[(R * N[(2.0 * N[ArcTan[N[Sqrt[N[(N[Power[N[Sin[N[(N[(phi1 - phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] + N[(N[(N[(N[Cos[phi1], $MachinePrecision] * N[Cos[phi2], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(lambda1 - lambda2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(lambda1 - lambda2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[(1.0 - N[(N[Power[N[Sin[N[(N[(phi1 - phi2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] + N[(N[(N[(N[Cos[phi1], $MachinePrecision] * N[Cos[phi2], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(lambda1 - lambda2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(lambda1 - lambda2), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[R_, lambda1_, lambda2_, phi1_, phi2_] := Block[{t$95$0 = N[Power[N[Sin[N[(-0.5 * N[(phi2 - phi1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(N[(lambda2 - lambda1), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(N[Cos[lambda2], $MachinePrecision] * N[(N[Cos[phi1], $MachinePrecision] * N[(N[Cos[phi2], $MachinePrecision] * N[Cos[lambda1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[Cos[phi1], $MachinePrecision] * N[(N[Cos[phi2], $MachinePrecision] * N[(N[Sin[lambda1], $MachinePrecision] * N[Sin[lambda2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Cos[phi2], $MachinePrecision] * 0.5), $MachinePrecision] * N[Cos[phi1], $MachinePrecision] + t$95$0), $MachinePrecision]}, N[(R * N[(2.0 * N[ArcTan[N[Sqrt[N[(N[Cos[phi1], $MachinePrecision] * N[(N[Cos[phi2], $MachinePrecision] * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[Sqrt[N[Power[N[(N[(N[Power[t$95$2, 3.0], $MachinePrecision] - N[Power[t$95$3, 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$2, 2.0], $MachinePrecision] + N[(N[Power[t$95$3, 2.0], $MachinePrecision] + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{{\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)}}{\sqrt{1 - \left({\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right)}}\right)
↓
\begin{array}{l}
t_0 := {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\\
t_1 := \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\\
t_2 := \mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_1\right)\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\\
t_3 := \mathsf{fma}\left(\cos \phi_2 \cdot 0.5, \cos \phi_1, t_0\right)\\
R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(t_1 \cdot t_1\right), t_0\right)}}{\sqrt{\sqrt{{\left(\frac{{t_2}^{3} - {t_3}^{3}}{{t_2}^{2} + \left({t_3}^{2} + t_2 \cdot t_3\right)}\right)}^{2}}}}\right)
\end{array}

Error

Bits error versus R

Bits error versus lambda1

Bits error versus lambda2

Bits error versus phi1

Bits error versus phi2

Derivation

  1. Initial program 24.0

    \[R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{{\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)}}{\sqrt{1 - \left({\sin \left(\frac{\phi_1 - \phi_2}{2}\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right)}}\right) \]

  2. Simplified24.0

    \[\leadsto \color{blue}{R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{1 - \mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}\right)} \]

  3. Applied egg-rr23.7

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\color{blue}{\sqrt{{\left(1 - \mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(0.5 - 0.5 \cdot \cos \left(\lambda_2 - \lambda_1\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{2}}}}}\right) \]

  4. Applied egg-rr23.4

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\sqrt{{\left(1 - \mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(0.5 - 0.5 \cdot \color{blue}{\mathsf{fma}\left(\cos \lambda_2, \cos \lambda_1, \sin \lambda_2 \cdot \sin \lambda_1\right)}\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{2}}}}\right) \]

  5. Taylor expanded in phi1 around inf 23.4

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\sqrt{{\color{blue}{\left(\left(0.5 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \cos \lambda_1\right)\right)\right) + \left(1 + 0.5 \cdot \left(\sin \lambda_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_2 \cdot \cos \phi_1\right)\right)\right)\right)\right) - \left(0.5 \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right) + {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}}^{2}}}}\right) \]

  6. Simplified23.4

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\sqrt{{\color{blue}{\left(\mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \lambda_1 \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right)\right), \mathsf{fma}\left(0.5, \left(\left(\sin \lambda_1 \cdot \sin \lambda_2\right) \cdot \cos \phi_2\right) \cdot \cos \phi_1, 1\right)\right) - \mathsf{fma}\left(0.5 \cdot \cos \phi_2, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}}^{2}}}}\right) \]

  7. Applied egg-rr23.4

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\sqrt{{\color{blue}{\left(\frac{{\left(\mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\left(\cos \lambda_1 \cdot \cos \phi_2\right) \cdot \cos \phi_1\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\right)}^{3} - {\left(\mathsf{fma}\left(0.5 \cdot \cos \phi_2, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{3}}{{\left(\mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\left(\cos \lambda_1 \cdot \cos \phi_2\right) \cdot \cos \phi_1\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\right)}^{2} + \left({\left(\mathsf{fma}\left(0.5 \cdot \cos \phi_2, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{2} + \mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\left(\cos \lambda_1 \cdot \cos \phi_2\right) \cdot \cos \phi_1\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right) \cdot \mathsf{fma}\left(0.5 \cdot \cos \phi_2, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}\right)}}^{2}}}}\right) \]

  8. Final simplification23.4

    \[\leadsto R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{\mathsf{fma}\left(\cos \phi_1, \cos \phi_2 \cdot \left(\sin \left(\frac{\lambda_2 - \lambda_1}{2}\right) \cdot \sin \left(\frac{\lambda_2 - \lambda_1}{2}\right)\right), {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)}}{\sqrt{\sqrt{{\left(\frac{{\left(\mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_1\right)\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\right)}^{3} - {\left(\mathsf{fma}\left(\cos \phi_2 \cdot 0.5, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{3}}{{\left(\mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_1\right)\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right)\right)}^{2} + \left({\left(\mathsf{fma}\left(\cos \phi_2 \cdot 0.5, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}^{2} + \mathsf{fma}\left(0.5, \cos \lambda_2 \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_1\right)\right), \mathsf{fma}\left(0.5, \cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right), 1\right)\right) \cdot \mathsf{fma}\left(\cos \phi_2 \cdot 0.5, \cos \phi_1, {\sin \left(-0.5 \cdot \left(\phi_2 - \phi_1\right)\right)}^{2}\right)\right)}\right)}^{2}}}}\right) \]

Reproduce

herbie shell --seed 2022153 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Distance on a great circle"
  :precision binary64
  (* R (* 2.0 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2.0)) 2.0) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2.0))) (sin (/ (- lambda1 lambda2) 2.0))))) (sqrt (- 1.0 (+ (pow (sin (/ (- phi1 phi2) 2.0)) 2.0) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2.0))) (sin (/ (- lambda1 lambda2) 2.0))))))))))