Average Error: 0.2 → 0.2
Time: 20.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}
double f(double B, double x) {
        double r930172 = x;
        double r930173 = 1.0;
        double r930174 = B;
        double r930175 = tan(r930174);
        double r930176 = r930173 / r930175;
        double r930177 = r930172 * r930176;
        double r930178 = -r930177;
        double r930179 = sin(r930174);
        double r930180 = r930173 / r930179;
        double r930181 = r930178 + r930180;
        return r930181;
}
↓
double f(double B, double x) {
        double r930182 = 1.0;
        double r930183 = B;
        double r930184 = sin(r930183);
        double r930185 = r930182 / r930184;
        double r930186 = 1.0;
        double r930187 = tan(r930183);
        double r930188 = x;
        double r930189 = r930182 * r930188;
        double r930190 = r930187 / r930189;
        double r930191 = r930186 / r930190;
        double r930192 = r930185 - r930191;
        return r930192;
}

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

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

  4. Applied clear-num0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))