Average Error: 0.2 → 0.2
Time: 22.1s
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 r433301 = x;
        double r433302 = 1.0;
        double r433303 = B;
        double r433304 = tan(r433303);
        double r433305 = r433302 / r433304;
        double r433306 = r433301 * r433305;
        double r433307 = -r433306;
        double r433308 = sin(r433303);
        double r433309 = r433302 / r433308;
        double r433310 = r433307 + r433309;
        return r433310;
}
↓
double f(double B, double x) {
        double r433311 = 1.0;
        double r433312 = B;
        double r433313 = sin(r433312);
        double r433314 = r433311 / r433313;
        double r433315 = x;
        double r433316 = r433315 / r433313;
        double r433317 = cos(r433312);
        double r433318 = r433316 * r433317;
        double r433319 = r433314 - r433318;
        return r433319;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019135 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))