Average Error: 0.2 → 0.2
Time: 14.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r55887 = x;
        double r55888 = 1.0;
        double r55889 = B;
        double r55890 = tan(r55889);
        double r55891 = r55888 / r55890;
        double r55892 = r55887 * r55891;
        double r55893 = -r55892;
        double r55894 = sin(r55889);
        double r55895 = r55888 / r55894;
        double r55896 = r55893 + r55895;
        return r55896;
}
↓
double f(double B, double x) {
        double r55897 = 1.0;
        double r55898 = 1.0;
        double r55899 = B;
        double r55900 = sin(r55899);
        double r55901 = r55898 / r55900;
        double r55902 = x;
        double r55903 = cos(r55899);
        double r55904 = r55902 * r55903;
        double r55905 = r55904 / r55900;
        double r55906 = r55901 - r55905;
        double r55907 = r55897 * r55906;
        return r55907;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Using strategy rm

  3. Applied associate-*r/0.2

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

  4. Applied distribute-neg-frac0.2

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

  5. Applied frac-add11.0

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

  6. Simplified11.0

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))