Average Error: 0.2 → 0.2
Time: 5.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r12138 = x;
        double r12139 = 1.0;
        double r12140 = B;
        double r12141 = tan(r12140);
        double r12142 = r12139 / r12141;
        double r12143 = r12138 * r12142;
        double r12144 = -r12143;
        double r12145 = sin(r12140);
        double r12146 = r12139 / r12145;
        double r12147 = r12144 + r12146;
        return r12147;
}
↓
double f(double B, double x) {
        double r12148 = 1.0;
        double r12149 = B;
        double r12150 = sin(r12149);
        double r12151 = r12148 / r12150;
        double r12152 = x;
        double r12153 = r12152 * r12148;
        double r12154 = r12153 / r12150;
        double r12155 = cos(r12149);
        double r12156 = r12154 * r12155;
        double r12157 = r12151 - r12156;
        return r12157;
}

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

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

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019346 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))