Average Error: 0.2 → 0.2
Time: 6.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)
double f(double B, double x) {
        double r18016 = x;
        double r18017 = 1.0;
        double r18018 = B;
        double r18019 = tan(r18018);
        double r18020 = r18017 / r18019;
        double r18021 = r18016 * r18020;
        double r18022 = -r18021;
        double r18023 = sin(r18018);
        double r18024 = r18017 / r18023;
        double r18025 = r18022 + r18024;
        return r18025;
}
↓
double f(double B, double x) {
        double r18026 = 1.0;
        double r18027 = B;
        double r18028 = sin(r18027);
        double r18029 = r18026 / r18028;
        double r18030 = x;
        double r18031 = cos(r18027);
        double r18032 = r18029 * r18031;
        double r18033 = r18030 * r18032;
        double r18034 = r18029 - r18033;
        return r18034;
}

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 tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

    \[\leadsto \frac{1}{\sin B} - x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))