Average Error: 0.2 → 0.2
Time: 24.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r595801 = x;
        double r595802 = 1.0;
        double r595803 = B;
        double r595804 = tan(r595803);
        double r595805 = r595802 / r595804;
        double r595806 = r595801 * r595805;
        double r595807 = -r595806;
        double r595808 = sin(r595803);
        double r595809 = r595802 / r595808;
        double r595810 = r595807 + r595809;
        return r595810;
}
↓
double f(double B, double x) {
        double r595811 = 1.0;
        double r595812 = B;
        double r595813 = cos(r595812);
        double r595814 = x;
        double r595815 = r595813 * r595814;
        double r595816 = r595811 - r595815;
        double r595817 = sin(r595812);
        double r595818 = r595816 / r595817;
        return r595818;
}

Error

Bits error versus B

Bits error versus x

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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

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

  3. Taylor expanded around -inf 0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019134 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))