Average Error: 0.2 → 0.2
Time: 20.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r22848 = x;
        double r22849 = 1.0;
        double r22850 = B;
        double r22851 = tan(r22850);
        double r22852 = r22849 / r22851;
        double r22853 = r22848 * r22852;
        double r22854 = -r22853;
        double r22855 = sin(r22850);
        double r22856 = r22849 / r22855;
        double r22857 = r22854 + r22856;
        return r22857;
}
↓
double f(double B, double x) {
        double r22858 = 1.0;
        double r22859 = B;
        double r22860 = sin(r22859);
        double r22861 = r22858 / r22860;
        double r22862 = x;
        double r22863 = r22862 * r22858;
        double r22864 = r22863 / r22860;
        double r22865 = cos(r22859);
        double r22866 = r22864 * r22865;
        double r22867 = r22861 - r22866;
        return r22867;
}

Error

Bits error versus B

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]
  3. Using strategy rm

  4. Applied associate-*r/0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot 1}{\tan B}}\]
  5. Using strategy rm

  6. Applied tan-quot0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x \cdot 1}{\color{blue}{\frac{\sin B}{\cos B}}}\]

  7. Applied associate-/r/0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot 1}{\sin B} \cdot \cos B}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity0.2

    \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\right)}\]

  10. Final simplification0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]

Reproduce

herbie shell --seed 2019326 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))