Average Error: 0.2 → 0.2
Time: 7.9s
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 r67086 = x;
        double r67087 = 1.0;
        double r67088 = B;
        double r67089 = tan(r67088);
        double r67090 = r67087 / r67089;
        double r67091 = r67086 * r67090;
        double r67092 = -r67091;
        double r67093 = sin(r67088);
        double r67094 = r67087 / r67093;
        double r67095 = r67092 + r67094;
        return r67095;
}
↓
double f(double B, double x) {
        double r67096 = 1.0;
        double r67097 = B;
        double r67098 = sin(r67097);
        double r67099 = r67096 / r67098;
        double r67100 = x;
        double r67101 = r67100 * r67096;
        double r67102 = r67101 / r67098;
        double r67103 = cos(r67097);
        double r67104 = r67102 * r67103;
        double r67105 = r67099 - r67104;
        return r67105;
}

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. 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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019318 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))