Average Error: 0.2 → 0.2
Time: 29.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r602769 = x;
        double r602770 = 1.0;
        double r602771 = B;
        double r602772 = tan(r602771);
        double r602773 = r602770 / r602772;
        double r602774 = r602769 * r602773;
        double r602775 = -r602774;
        double r602776 = sin(r602771);
        double r602777 = r602770 / r602776;
        double r602778 = r602775 + r602777;
        return r602778;
}
↓
double f(double B, double x) {
        double r602779 = 1.0;
        double r602780 = B;
        double r602781 = sin(r602780);
        double r602782 = r602779 / r602781;
        double r602783 = x;
        double r602784 = r602783 / r602781;
        double r602785 = cos(r602780);
        double r602786 = r602784 * r602785;
        double r602787 = r602782 - r602786;
        return r602787;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))