Average Error: 0.2 → 0.3
Time: 16.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r45087 = x;
        double r45088 = 1.0;
        double r45089 = B;
        double r45090 = tan(r45089);
        double r45091 = r45088 / r45090;
        double r45092 = r45087 * r45091;
        double r45093 = -r45092;
        double r45094 = sin(r45089);
        double r45095 = r45088 / r45094;
        double r45096 = r45093 + r45095;
        return r45096;
}
↓
double f(double B, double x) {
        double r45097 = 1.0;
        double r45098 = B;
        double r45099 = sin(r45098);
        double r45100 = r45097 / r45099;
        double r45101 = x;
        double r45102 = r45101 * r45100;
        double r45103 = cos(r45098);
        double r45104 = r45102 * r45103;
        double r45105 = r45100 - r45104;
        return r45105;
}

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 tan-quot0.3

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

  5. Applied associate-/r/0.3

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

  6. Applied associate-*r*0.3

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

  7. Final simplification0.3

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

Reproduce

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