Average Error: 0.2 → 0.6
Time: 27.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \left(\frac{x}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}} \cdot \frac{\cos B}{\sqrt[3]{\sin B}}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \left(\frac{x}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}} \cdot \frac{\cos B}{\sqrt[3]{\sin B}}\right)
double f(double B, double x) {
        double r2434993 = x;
        double r2434994 = 1.0;
        double r2434995 = B;
        double r2434996 = tan(r2434995);
        double r2434997 = r2434994 / r2434996;
        double r2434998 = r2434993 * r2434997;
        double r2434999 = -r2434998;
        double r2435000 = sin(r2434995);
        double r2435001 = r2434994 / r2435000;
        double r2435002 = r2434999 + r2435001;
        return r2435002;
}
↓
double f(double B, double x) {
        double r2435003 = 1.0;
        double r2435004 = B;
        double r2435005 = sin(r2435004);
        double r2435006 = r2435003 / r2435005;
        double r2435007 = x;
        double r2435008 = cbrt(r2435005);
        double r2435009 = r2435008 * r2435008;
        double r2435010 = r2435007 / r2435009;
        double r2435011 = cos(r2435004);
        double r2435012 = r2435011 / r2435008;
        double r2435013 = r2435010 * r2435012;
        double r2435014 = r2435003 * r2435013;
        double r2435015 = r2435006 - r2435014;
        return r2435015;
}

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

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

  3. Taylor expanded around inf 0.2

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

  5. Applied add-cube-cbrt0.6

    \[\leadsto \frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\color{blue}{\left(\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}\right) \cdot \sqrt[3]{\sin B}}}\]

  6. Applied times-frac0.6

    \[\leadsto \frac{1}{\sin B} - 1 \cdot \color{blue}{\left(\frac{x}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}} \cdot \frac{\cos B}{\sqrt[3]{\sin B}}\right)}\]

  7. Final simplification0.6

    \[\leadsto \frac{1}{\sin B} - 1 \cdot \left(\frac{x}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}} \cdot \frac{\cos B}{\sqrt[3]{\sin B}}\right)\]

Reproduce

herbie shell --seed 2019200 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))