Average Error: 0.2 → 0.2
Time: 6.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{1}{\frac{\tan B}{x \cdot 1}}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{1}{\frac{\tan B}{x \cdot 1}}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r44187 = x;
        double r44188 = 1.0;
        double r44189 = B;
        double r44190 = tan(r44189);
        double r44191 = r44188 / r44190;
        double r44192 = r44187 * r44191;
        double r44193 = -r44192;
        double r44194 = sin(r44189);
        double r44195 = r44188 / r44194;
        double r44196 = r44193 + r44195;
        return r44196;
}
↓
double f(double B, double x) {
        double r44197 = 1.0;
        double r44198 = B;
        double r44199 = tan(r44198);
        double r44200 = x;
        double r44201 = 1.0;
        double r44202 = r44200 * r44201;
        double r44203 = r44199 / r44202;
        double r44204 = r44197 / r44203;
        double r44205 = -r44204;
        double r44206 = sin(r44198);
        double r44207 = r44201 / r44206;
        double r44208 = r44205 + r44207;
        return r44208;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied clear-num0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))