Average Error: 0.2 → 0.3
Time: 18.1s
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 r27944 = x;
        double r27945 = 1.0;
        double r27946 = B;
        double r27947 = tan(r27946);
        double r27948 = r27945 / r27947;
        double r27949 = r27944 * r27948;
        double r27950 = -r27949;
        double r27951 = sin(r27946);
        double r27952 = r27945 / r27951;
        double r27953 = r27950 + r27952;
        return r27953;
}
↓
double f(double B, double x) {
        double r27954 = x;
        double r27955 = 1.0;
        double r27956 = B;
        double r27957 = sin(r27956);
        double r27958 = r27955 / r27957;
        double r27959 = r27954 * r27958;
        double r27960 = cos(r27956);
        double r27961 = r27959 * r27960;
        double r27962 = -r27961;
        double r27963 = r27962 + r27958;
        return r27963;
}

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