Average Error: 0.2 → 0.2
Time: 16.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{\cos B \cdot x}{\sin B} \cdot 1\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{\cos B \cdot x}{\sin B} \cdot 1
double f(double B, double x) {
        double r22679 = x;
        double r22680 = 1.0;
        double r22681 = B;
        double r22682 = tan(r22681);
        double r22683 = r22680 / r22682;
        double r22684 = r22679 * r22683;
        double r22685 = -r22684;
        double r22686 = sin(r22681);
        double r22687 = r22680 / r22686;
        double r22688 = r22685 + r22687;
        return r22688;
}
↓
double f(double B, double x) {
        double r22689 = 1.0;
        double r22690 = B;
        double r22691 = sin(r22690);
        double r22692 = r22689 / r22691;
        double r22693 = cos(r22690);
        double r22694 = x;
        double r22695 = r22693 * r22694;
        double r22696 = r22695 / r22691;
        double r22697 = r22696 * r22689;
        double r22698 = r22692 - r22697;
        return r22698;
}

Error

Bits error versus B

Bits error versus x

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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-quot0.2

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

  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. Simplified0.2

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))