?

Average Error: 20.21% → 0.27%
Time: 1.0min
Precision: binary64
Cost: 110080

?

\[\tan^{-1}_* \frac{\sin \left(\lambda_1 - \lambda_2\right) \cdot \cos \phi_2}{\cos \phi_1 \cdot \sin \phi_2 - \left(\sin \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)} \]
↓
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_2, \sin \lambda_1, \sin \left(-\lambda_2\right) \cdot \cos \lambda_1\right)}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \left(\sin \phi_1 \cdot \left(-\cos \phi_2\right)\right) \cdot \mathsf{fma}\left(\cos \lambda_1, \cos \lambda_2, \sin \lambda_1 \cdot \sin \lambda_2\right)\right)} \]
(FPCore (lambda1 lambda2 phi1 phi2)
 :precision binary64
 (atan2
  (* (sin (- lambda1 lambda2)) (cos phi2))
  (-
   (* (cos phi1) (sin phi2))
   (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
↓
(FPCore (lambda1 lambda2 phi1 phi2)
 :precision binary64
 (atan2
  (*
   (cos phi2)
   (fma (cos lambda2) (sin lambda1) (* (sin (- lambda2)) (cos lambda1))))
  (fma
   (sin phi2)
   (cos phi1)
   (*
    (* (sin phi1) (- (cos phi2)))
    (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
double code(double lambda1, double lambda2, double phi1, double phi2) {
	return atan2((sin((lambda1 - lambda2)) * cos(phi2)), ((cos(phi1) * sin(phi2)) - ((sin(phi1) * cos(phi2)) * cos((lambda1 - lambda2)))));
}
↓
double code(double lambda1, double lambda2, double phi1, double phi2) {
	return atan2((cos(phi2) * fma(cos(lambda2), sin(lambda1), (sin(-lambda2) * cos(lambda1)))), fma(sin(phi2), cos(phi1), ((sin(phi1) * -cos(phi2)) * fma(cos(lambda1), cos(lambda2), (sin(lambda1) * sin(lambda2))))));
}

function code(lambda1, lambda2, phi1, phi2)
	return atan(Float64(sin(Float64(lambda1 - lambda2)) * cos(phi2)), Float64(Float64(cos(phi1) * sin(phi2)) - Float64(Float64(sin(phi1) * cos(phi2)) * cos(Float64(lambda1 - lambda2)))))
end
↓
function code(lambda1, lambda2, phi1, phi2)
	return atan(Float64(cos(phi2) * fma(cos(lambda2), sin(lambda1), Float64(sin(Float64(-lambda2)) * cos(lambda1)))), fma(sin(phi2), cos(phi1), Float64(Float64(sin(phi1) * Float64(-cos(phi2))) * fma(cos(lambda1), cos(lambda2), Float64(sin(lambda1) * sin(lambda2))))))
end

code[lambda1_, lambda2_, phi1_, phi2_] := N[ArcTan[N[(N[Sin[N[(lambda1 - lambda2), $MachinePrecision]], $MachinePrecision] * N[Cos[phi2], $MachinePrecision]), $MachinePrecision] / N[(N[(N[Cos[phi1], $MachinePrecision] * N[Sin[phi2], $MachinePrecision]), $MachinePrecision] - N[(N[(N[Sin[phi1], $MachinePrecision] * N[Cos[phi2], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(lambda1 - lambda2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[lambda1_, lambda2_, phi1_, phi2_] := N[ArcTan[N[(N[Cos[phi2], $MachinePrecision] * N[(N[Cos[lambda2], $MachinePrecision] * N[Sin[lambda1], $MachinePrecision] + N[(N[Sin[(-lambda2)], $MachinePrecision] * N[Cos[lambda1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Sin[phi2], $MachinePrecision] * N[Cos[phi1], $MachinePrecision] + N[(N[(N[Sin[phi1], $MachinePrecision] * (-N[Cos[phi2], $MachinePrecision])), $MachinePrecision] * N[(N[Cos[lambda1], $MachinePrecision] * N[Cos[lambda2], $MachinePrecision] + N[(N[Sin[lambda1], $MachinePrecision] * N[Sin[lambda2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

\tan^{-1}_* \frac{\sin \left(\lambda_1 - \lambda_2\right) \cdot \cos \phi_2}{\cos \phi_1 \cdot \sin \phi_2 - \left(\sin \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)}
↓
\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_2, \sin \lambda_1, \sin \left(-\lambda_2\right) \cdot \cos \lambda_1\right)}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \left(\sin \phi_1 \cdot \left(-\cos \phi_2\right)\right) \cdot \mathsf{fma}\left(\cos \lambda_1, \cos \lambda_2, \sin \lambda_1 \cdot \sin \lambda_2\right)\right)}

Error?

Derivation?

  1. Initial program 20.21

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

  2. Applied egg-rr10.49

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

  3. Simplified10.49

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

    [Start]10.49

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

    +-commutative [=>]10.49

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

    distribute-lft-neg-in [<=]10.49

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

    distribute-rgt-neg-in [=>]10.49

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

    sin-neg [<=]10.49

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

    cos-neg [<=]10.49

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

    fma-def [=>]10.49

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

    *-commutative [=>]10.49

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

    cos-neg [=>]10.49

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

  4. Applied egg-rr0.28

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

  5. Simplified0.27

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

    [Start]0.28

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

    associate-+r+ [=>]0.28

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

    +-commutative [=>]0.28

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

    *-commutative [=>]0.28

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

    fma-def [=>]0.27

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

    distribute-lft-out [=>]0.27

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

    distribute-rgt-neg-out [=>]0.27

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

    *-commutative [=>]0.27

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

    distribute-rgt-neg-in [=>]0.27

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

    fma-def [=>]0.27

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

  6. Taylor expanded in lambda1 around inf 0.27

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

  7. Simplified0.27

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

    [Start]0.27

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

    +-commutative [=>]0.27

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

    *-commutative [=>]0.27

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

    fma-def [=>]0.27

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

  8. Final simplification0.27

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

Alternatives

Alternative 1
Error0.27%
Cost103744
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1 - \cos \lambda_1 \cdot \sin \lambda_2\right)}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \left(\sin \phi_1 \cdot \left(-\cos \phi_2\right)\right) \cdot \mathsf{fma}\left(\cos \lambda_1, \cos \lambda_2, \sin \lambda_1 \cdot \sin \lambda_2\right)\right)} \]
Alternative 2
Error5.61%
Cost97481
\[\begin{array}{l} t_0 := \cos \lambda_2 \cdot \sin \lambda_1\\ \mathbf{if}\;\phi_2 \leq -9.2 \cdot 10^{-7} \lor \neg \left(\phi_2 \leq 10^{-17}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, \sin \left(-\lambda_2\right), t_0\right)}{\sin \phi_2 \cdot \cos \phi_1 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0 - \cos \lambda_1 \cdot \sin \lambda_2}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \left(\sin \phi_1 \cdot \left(-\cos \phi_2\right)\right) \cdot \mathsf{fma}\left(\cos \lambda_1, \cos \lambda_2, \sin \lambda_1 \cdot \sin \lambda_2\right)\right)}\\ \end{array} \]
Alternative 3
Error0.27%
Cost97472
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, \sin \left(-\lambda_2\right), \cos \lambda_2 \cdot \sin \lambda_1\right)}{\sin \phi_2 \cdot \cos \phi_1 - \left(\sin \lambda_1 \cdot \sin \lambda_2 + \cos \lambda_2 \cdot \cos \lambda_1\right) \cdot \left(\cos \phi_2 \cdot \sin \phi_1\right)} \]
Alternative 4
Error0.27%
Cost97472
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_2, \sin \lambda_1, \sin \left(-\lambda_2\right) \cdot \cos \lambda_1\right)}{\sin \phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2 + \cos \lambda_2 \cdot \cos \lambda_1\right)\right)} \]
Alternative 5
Error5.61%
Cost97417
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, \sin \left(-\lambda_2\right), \cos \lambda_2 \cdot \sin \lambda_1\right)\\ \mathbf{if}\;\phi_2 \leq -1.55 \cdot 10^{-6} \lor \neg \left(\phi_2 \leq 1.45 \cdot 10^{-17}\right):\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2 \cdot \cos \phi_1 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\mathsf{fma}\left(\phi_2, \cos \phi_1, \sin \phi_1 \cdot \left(-\mathsf{fma}\left(\sin \lambda_2, \sin \lambda_1, \cos \lambda_2 \cdot \cos \lambda_1\right)\right)\right)}\\ \end{array} \]
Alternative 6
Error7.18%
Cost78281
\[\begin{array}{l} t_0 := \sin \left(-\lambda_2\right)\\ \mathbf{if}\;\phi_2 \leq -5.4 \cdot 10^{-62} \lor \neg \left(\phi_2 \leq 2.45 \cdot 10^{-19}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, t_0, \cos \lambda_2 \cdot \sin \lambda_1\right)}{\sin \phi_2 \cdot \cos \phi_1 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_2, \sin \lambda_1, t_0 \cdot \cos \lambda_1\right)}{\sin \phi_1 \cdot \left(\sin \lambda_2 \cdot \left(-\sin \lambda_1\right) - \cos \lambda_2 \cdot \cos \lambda_1\right)}\\ \end{array} \]
Alternative 7
Error7.21%
Cost78217
\[\begin{array}{l} \mathbf{if}\;\phi_2 \leq -7.2 \cdot 10^{-63} \lor \neg \left(\phi_2 \leq 1.62 \cdot 10^{-18}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1 - \cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_2, \sin \lambda_1, \sin \left(-\lambda_2\right) \cdot \cos \lambda_1\right)}{\sin \phi_1 \cdot \left(\sin \lambda_2 \cdot \left(-\sin \lambda_1\right) - \cos \lambda_2 \cdot \cos \lambda_1\right)}\\ \end{array} \]
Alternative 8
Error13.84%
Cost71944
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_1 \leq -2.9 \cdot 10^{-34}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \cos \phi_2 \cdot \left(\sin \phi_1 \cdot \left(-\cos \left(\lambda_1 - \lambda_2\right)\right)\right)\right)}\\ \mathbf{elif}\;\phi_1 \leq 5 \cdot 10^{-48}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2 \cdot \cos \phi_1 - \left(\sin \lambda_1 \cdot \sin \lambda_2 + \cos \lambda_2 \cdot \cos \lambda_1\right) \cdot \left(\cos \phi_2 \cdot \sin \phi_1\right)}\\ \end{array} \]
Alternative 9
Error10.49%
Cost71680
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1 - \cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)} \]
Alternative 10
Error13.94%
Cost58692
\[\begin{array}{l} t_0 := \cos \left(\lambda_1 - \lambda_2\right)\\ t_1 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_1 \leq -9.6 \cdot 10^{-31}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{\mathsf{fma}\left(\sin \phi_2, \cos \phi_1, \cos \phi_2 \cdot \left(\sin \phi_1 \cdot \left(-t_0\right)\right)\right)}\\ \mathbf{elif}\;\phi_1 \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{\sin \phi_2 \cdot \cos \phi_1 - \cos \phi_2 \cdot \left(\sin \phi_1 \cdot t_0\right)}\\ \end{array} \]
Alternative 11
Error27.7%
Cost52692
\[\begin{array}{l} t_0 := \cos \left(\lambda_1 - \lambda_2\right)\\ t_1 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ t_2 := \sin \phi_2 \cdot \cos \phi_1\\ t_3 := \sin \left(-\lambda_2\right)\\ t_4 := \tan^{-1}_* \frac{t_1}{t_2 - \sin \phi_1 \cdot t_0}\\ t_5 := \cos \phi_2 \cdot \sin \phi_1\\ \mathbf{if}\;\lambda_2 \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, t_3, \cos \lambda_2 \cdot \sin \lambda_1\right)}{\sin \phi_2}\\ \mathbf{elif}\;\lambda_2 \leq -8 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;\lambda_2 \leq -2 \cdot 10^{-72}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_2 - t_5}\\ \mathbf{elif}\;\lambda_2 \leq 5.2 \cdot 10^{-154}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \lambda_1}{t_2 - t_5 \cdot t_0}\\ \mathbf{elif}\;\lambda_2 \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot t_3}{t_2 - \cos \lambda_2 \cdot t_5}\\ \end{array} \]
Alternative 12
Error27.72%
Cost52692
\[\begin{array}{l} t_0 := \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)\\ t_1 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ t_2 := \sin \phi_2 \cdot \cos \phi_1\\ t_3 := \sin \left(-\lambda_2\right)\\ t_4 := \tan^{-1}_* \frac{t_1}{t_2 - t_0}\\ t_5 := \cos \phi_2 \cdot \sin \phi_1\\ \mathbf{if}\;\lambda_2 \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, t_3, \cos \lambda_2 \cdot \sin \lambda_1\right)}{\sin \phi_2}\\ \mathbf{elif}\;\lambda_2 \leq -7.4 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;\lambda_2 \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_2 - t_5}\\ \mathbf{elif}\;\lambda_2 \leq 1.1 \cdot 10^{-155}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \lambda_1}{t_2 - \cos \phi_2 \cdot t_0}\\ \mathbf{elif}\;\lambda_2 \leq 3 \cdot 10^{-6}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot t_3}{t_2 - \cos \lambda_2 \cdot t_5}\\ \end{array} \]
Alternative 13
Error20.39%
Cost52496
\[\begin{array}{l} t_0 := \sin \phi_2 \cdot \cos \phi_1\\ t_1 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ t_2 := \tan^{-1}_* \frac{t_1}{t_0 - \cos \lambda_1 \cdot \left(\cos \phi_2 \cdot \sin \phi_1\right)}\\ \mathbf{if}\;\lambda_1 \leq -0.000135:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\lambda_1 \leq 7.3 \cdot 10^{-7}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_0 - \sin \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_2\right)}\\ \mathbf{elif}\;\lambda_1 \leq 1.9 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\lambda_1 \leq 1.25 \cdot 10^{+298}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_0 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \end{array} \]
Alternative 14
Error20.63%
Cost52492
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \phi_1\\ t_1 := \cos \left(\lambda_1 - \lambda_2\right)\\ t_2 := \cos \phi_2 \cdot \sin \lambda_1\\ t_3 := \sin \phi_2 \cdot \cos \phi_1\\ \mathbf{if}\;\lambda_1 \leq -0.00182:\\ \;\;\;\;\tan^{-1}_* \frac{t_2}{t_3 - t_0 \cdot t_1}\\ \mathbf{elif}\;\lambda_1 \leq 3.35:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{t_3 - \cos \lambda_2 \cdot t_0}\\ \mathbf{elif}\;\lambda_1 \leq 1.5 \cdot 10^{+102}:\\ \;\;\;\;\tan^{-1}_* \frac{t_2}{t_3 - \cos \phi_2 \cdot \left(\sin \phi_1 \cdot t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 15
Error20.64%
Cost52492
\[\begin{array}{l} t_0 := \cos \left(\lambda_1 - \lambda_2\right)\\ t_1 := \cos \phi_2 \cdot \sin \lambda_1\\ t_2 := \sin \phi_2 \cdot \cos \phi_1\\ \mathbf{if}\;\lambda_1 \leq -0.0235:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_2 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot t_0}\\ \mathbf{elif}\;\lambda_1 \leq 3.35:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{t_2 - \sin \phi_1 \cdot \left(\cos \phi_2 \cdot \cos \lambda_2\right)}\\ \mathbf{elif}\;\lambda_1 \leq 2.7 \cdot 10^{+101}:\\ \;\;\;\;\tan^{-1}_* \frac{t_1}{t_2 - \cos \phi_2 \cdot \left(\sin \phi_1 \cdot t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 16
Error13.94%
Cost52489
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -3 \cdot 10^{-31} \lor \neg \left(\phi_1 \leq 4.6 \cdot 10^{-48}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \cos \phi_2 \cdot \left(\sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 17
Error13.93%
Cost52488
\[\begin{array}{l} t_0 := \sin \phi_2 \cdot \cos \phi_1\\ t_1 := \cos \left(\lambda_1 - \lambda_2\right)\\ t_2 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_1 \leq -3.7 \cdot 10^{-32}:\\ \;\;\;\;\tan^{-1}_* \frac{t_2}{t_0 - \left(\cos \phi_2 \cdot \sin \phi_1\right) \cdot t_1}\\ \mathbf{elif}\;\phi_1 \leq 5 \cdot 10^{-48}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_2}{t_0 - \cos \phi_2 \cdot \left(\sin \phi_1 \cdot t_1\right)}\\ \end{array} \]
Alternative 18
Error26.53%
Cost52233
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -9.2 \cdot 10^{-38} \lor \neg \left(\phi_1 \leq 7.8 \cdot 10^{-11}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1\right) - \cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 19
Error26.47%
Cost52041
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -1.36 \cdot 10^{-33} \lor \neg \left(\phi_1 \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, \sin \left(-\lambda_2\right), \cos \lambda_2 \cdot \sin \lambda_1\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 20
Error26.46%
Cost45961
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -2.3 \cdot 10^{-33} \lor \neg \left(\phi_1 \leq 7 \cdot 10^{-9}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1 - \cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 21
Error28.32%
Cost45705
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -9.6 \cdot 10^{-31} \lor \neg \left(\phi_1 \leq 1600\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_1 \cdot \left(-\cos \left(\lambda_1 - \lambda_2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \sin \lambda_1 - \cos \lambda_1 \cdot \sin \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 22
Error33.38%
Cost45513
\[\begin{array}{l} \mathbf{if}\;\phi_2 \leq -0.01 \lor \neg \left(\phi_2 \leq 0.00135\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \mathsf{fma}\left(\cos \lambda_1, \sin \left(-\lambda_2\right), \sin \lambda_1\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \end{array} \]
Alternative 23
Error34.81%
Cost39940
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_2 \leq -1800000:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2 \cdot \left(-0.5 \cdot \left(\phi_1 \cdot \phi_1\right) + 1\right) - \cos \left(\lambda_2 - \lambda_1\right) \cdot \left(\cos \phi_2 \cdot \phi_1\right)}\\ \mathbf{elif}\;\phi_2 \leq 0.00158:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2}\\ \end{array} \]
Alternative 24
Error34.07%
Cost39561
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_1 \leq -0.00095 \lor \neg \left(\phi_1 \leq 0.0037\right):\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_1 \cdot \left(-\cos \left(\lambda_1 - \lambda_2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2 - \cos \left(\lambda_2 - \lambda_1\right) \cdot \left(\cos \phi_2 \cdot \phi_1\right)}\\ \end{array} \]
Alternative 25
Error34.07%
Cost39560
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_2 \leq -0.0235:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\mathsf{log1p}\left(-1 + e^{\sin \phi_2}\right)}\\ \mathbf{elif}\;\phi_2 \leq 0.00158:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\phi_2 \cdot \cos \phi_1 - \sin \phi_1 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2}\\ \end{array} \]
Alternative 26
Error36.17%
Cost32969
\[\begin{array}{l} t_0 := \cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_1 \leq -9.6 \cdot 10^{-31} \lor \neg \left(\phi_1 \leq 1550\right):\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_1 \cdot \left(-\cos \left(\lambda_1 - \lambda_2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0}{\sin \phi_2}\\ \end{array} \]
Alternative 27
Error46.1%
Cost32905
\[\begin{array}{l} \mathbf{if}\;\phi_1 \leq -1.2 \cdot 10^{+97} \lor \neg \left(\phi_1 \leq 14000\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(-\lambda_2\right)}{\sin \phi_1 \cdot \left(-\cos \left(\lambda_1 - \lambda_2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 28
Error50.65%
Cost32644
\[\begin{array}{l} \mathbf{if}\;\lambda_2 \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\cos \lambda_2 \cdot \lambda_1 - \sin \lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 29
Error56.44%
Cost26185
\[\begin{array}{l} \mathbf{if}\;\lambda_2 \leq -5.3 \cdot 10^{-14} \lor \neg \left(\lambda_2 \leq 2 \cdot 10^{-129}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(-\lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \lambda_1}{\sin \phi_2}\\ \end{array} \]
Alternative 30
Error61.25%
Cost26120
\[\begin{array}{l} \mathbf{if}\;\lambda_2 \leq -8.8 \cdot 10^{-14}:\\ \;\;\;\;\tan^{-1}_* \frac{\sin \left(-\lambda_2\right)}{\sin \phi_2}\\ \mathbf{elif}\;\lambda_2 \leq 0.0023:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \lambda_1}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 31
Error65.76%
Cost25988
\[\begin{array}{l} t_0 := \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_2 \leq 4.6 \cdot 10^{+25}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot t_0}{\phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\left|t_0\right|}{\sin \phi_2}\\ \end{array} \]
Alternative 32
Error50.35%
Cost25984
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2} \]
Alternative 33
Error66.45%
Cost20100
\[\begin{array}{l} t_0 := \sin \left(\lambda_1 - \lambda_2\right)\\ \mathbf{if}\;\phi_2 \leq 4000000:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot t_0}{\phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{t_0 \cdot \left(1 + -0.5 \cdot \left(\phi_2 \cdot \phi_2\right)\right)}{\sin \phi_2}\\ \end{array} \]
Alternative 34
Error66.09%
Cost19716
\[\begin{array}{l} \mathbf{if}\;\phi_2 \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\phi_2}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(-1 + \tan^{-1}_* \frac{\sin \lambda_1}{\sin \phi_2}\right)\\ \end{array} \]
Alternative 35
Error70.42%
Cost19657
\[\begin{array}{l} \mathbf{if}\;\lambda_2 \leq -7.5 \cdot 10^{-20} \lor \neg \left(\lambda_2 \leq 5.1 \cdot 10^{-54}\right):\\ \;\;\;\;\tan^{-1}_* \frac{\sin \left(-\lambda_2\right)}{\sin \phi_2}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1}_* \frac{\sin \lambda_1}{\sin \phi_2}\\ \end{array} \]
Alternative 36
Error68.04%
Cost19456
\[\tan^{-1}_* \frac{\sin \left(\lambda_1 - \lambda_2\right)}{\sin \phi_2} \]
Alternative 37
Error76.12%
Cost19328
\[\tan^{-1}_* \frac{\sin \lambda_1}{\sin \phi_2} \]

Error

Reproduce?

herbie shell --seed 2023104 
(FPCore (lambda1 lambda2 phi1 phi2)
  :name "Bearing on a great circle"
  :precision binary64
  (atan2 (* (sin (- lambda1 lambda2)) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))))