Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \frac{1 - x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \frac{1 - x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r113067 = x;
        double r113068 = 1.0;
        double r113069 = B;
        double r113070 = tan(r113069);
        double r113071 = r113068 / r113070;
        double r113072 = r113067 * r113071;
        double r113073 = -r113072;
        double r113074 = sin(r113069);
        double r113075 = r113068 / r113074;
        double r113076 = r113073 + r113075;
        return r113076;
}
↓
double f(double B, double x) {
        double r113077 = 1.0;
        double r113078 = 1.0;
        double r113079 = x;
        double r113080 = B;
        double r113081 = cos(r113080);
        double r113082 = r113079 * r113081;
        double r113083 = r113078 - r113082;
        double r113084 = sin(r113080);
        double r113085 = r113083 / r113084;
        double r113086 = r113077 * r113085;
        return r113086;
}

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. Taylor expanded around inf 0.2

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

  3. Simplified0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))