Average Error: 0.2 → 0.3
Time: 17.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r53914 = x;
        double r53915 = 1.0;
        double r53916 = B;
        double r53917 = tan(r53916);
        double r53918 = r53915 / r53917;
        double r53919 = r53914 * r53918;
        double r53920 = -r53919;
        double r53921 = sin(r53916);
        double r53922 = r53915 / r53921;
        double r53923 = r53920 + r53922;
        return r53923;
}
↓
double f(double B, double x) {
        double r53924 = x;
        double r53925 = 1.0;
        double r53926 = B;
        double r53927 = sin(r53926);
        double r53928 = r53925 / r53927;
        double r53929 = r53924 * r53928;
        double r53930 = cos(r53926);
        double r53931 = r53929 * r53930;
        double r53932 = -r53931;
        double r53933 = r53932 + r53928;
        return r53933;
}

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 tan-quot0.3

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

  4. Applied associate-/r/0.3

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

  5. Applied associate-*r*0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))