Average Error: 0.2 → 0.6
Time: 28.7s
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 r2202655 = x;
        double r2202656 = 1.0;
        double r2202657 = B;
        double r2202658 = tan(r2202657);
        double r2202659 = r2202656 / r2202658;
        double r2202660 = r2202655 * r2202659;
        double r2202661 = -r2202660;
        double r2202662 = sin(r2202657);
        double r2202663 = r2202656 / r2202662;
        double r2202664 = r2202661 + r2202663;
        return r2202664;
}
↓
double f(double B, double x) {
        double r2202665 = 1.0;
        double r2202666 = B;
        double r2202667 = sin(r2202666);
        double r2202668 = r2202665 / r2202667;
        double r2202669 = x;
        double r2202670 = cbrt(r2202667);
        double r2202671 = r2202670 * r2202670;
        double r2202672 = r2202669 / r2202671;
        double r2202673 = cos(r2202666);
        double r2202674 = r2202673 / r2202670;
        double r2202675 = r2202672 * r2202674;
        double r2202676 = r2202665 * r2202675;
        double r2202677 = r2202668 - r2202676;
        return r2202677;
}

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))))