Average Error: 0.2 → 0.2
Time: 19.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r24727 = x;
        double r24728 = 1.0;
        double r24729 = B;
        double r24730 = tan(r24729);
        double r24731 = r24728 / r24730;
        double r24732 = r24727 * r24731;
        double r24733 = -r24732;
        double r24734 = sin(r24729);
        double r24735 = r24728 / r24734;
        double r24736 = r24733 + r24735;
        return r24736;
}
↓
double f(double B, double x) {
        double r24737 = 1.0;
        double r24738 = 1.0;
        double r24739 = B;
        double r24740 = sin(r24739);
        double r24741 = r24738 / r24740;
        double r24742 = x;
        double r24743 = cos(r24739);
        double r24744 = r24742 * r24743;
        double r24745 = r24744 / r24740;
        double r24746 = r24741 - r24745;
        double r24747 = r24737 * r24746;
        return r24747;
}

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. Taylor expanded around inf 0.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))