Average Error: 0.2 → 0.2
Time: 5.2s
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 r44132 = x;
        double r44133 = 1.0;
        double r44134 = B;
        double r44135 = tan(r44134);
        double r44136 = r44133 / r44135;
        double r44137 = r44132 * r44136;
        double r44138 = -r44137;
        double r44139 = sin(r44134);
        double r44140 = r44133 / r44139;
        double r44141 = r44138 + r44140;
        return r44141;
}
↓
double f(double B, double x) {
        double r44142 = 1.0;
        double r44143 = 1.0;
        double r44144 = x;
        double r44145 = B;
        double r44146 = cos(r44145);
        double r44147 = r44144 * r44146;
        double r44148 = r44143 - r44147;
        double r44149 = sin(r44145);
        double r44150 = r44148 / r44149;
        double r44151 = r44142 * r44150;
        return r44151;
}

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 2019344 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))