Average Error: 0.2 → 0.2
Time: 17.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r28088 = x;
        double r28089 = 1.0;
        double r28090 = B;
        double r28091 = tan(r28090);
        double r28092 = r28089 / r28091;
        double r28093 = r28088 * r28092;
        double r28094 = -r28093;
        double r28095 = sin(r28090);
        double r28096 = r28089 / r28095;
        double r28097 = r28094 + r28096;
        return r28097;
}
↓
double f(double B, double x) {
        double r28098 = 1.0;
        double r28099 = B;
        double r28100 = sin(r28099);
        double r28101 = r28098 / r28100;
        double r28102 = x;
        double r28103 = r28102 / r28100;
        double r28104 = r28098 * r28103;
        double r28105 = cos(r28099);
        double r28106 = r28104 * r28105;
        double r28107 = r28101 - r28106;
        return r28107;
}

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. Applied associate-*r*0.3

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))