Average Error: 0.2 → 0.2
Time: 20.8s
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 r1250812 = x;
        double r1250813 = 1.0;
        double r1250814 = B;
        double r1250815 = tan(r1250814);
        double r1250816 = r1250813 / r1250815;
        double r1250817 = r1250812 * r1250816;
        double r1250818 = -r1250817;
        double r1250819 = sin(r1250814);
        double r1250820 = r1250813 / r1250819;
        double r1250821 = r1250818 + r1250820;
        return r1250821;
}
↓
double f(double B, double x) {
        double r1250822 = 1.0;
        double r1250823 = B;
        double r1250824 = sin(r1250823);
        double r1250825 = r1250822 / r1250824;
        double r1250826 = x;
        double r1250827 = r1250826 / r1250824;
        double r1250828 = cos(r1250823);
        double r1250829 = r1250827 * r1250828;
        double r1250830 = r1250825 - r1250829;
        return r1250830;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019138 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))