Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r33015 = x;
        double r33016 = 1.0;
        double r33017 = B;
        double r33018 = tan(r33017);
        double r33019 = r33016 / r33018;
        double r33020 = r33015 * r33019;
        double r33021 = -r33020;
        double r33022 = sin(r33017);
        double r33023 = r33016 / r33022;
        double r33024 = r33021 + r33023;
        return r33024;
}
↓
double f(double B, double x) {
        double r33025 = 1.0;
        double r33026 = x;
        double r33027 = B;
        double r33028 = cos(r33027);
        double r33029 = r33026 * r33028;
        double r33030 = sin(r33027);
        double r33031 = r33029 / r33030;
        double r33032 = r33025 * r33031;
        double r33033 = -r33032;
        double r33034 = r33025 / r33030;
        double r33035 = r33033 + r33034;
        return r33035;
}

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. Taylor expanded around inf 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))