Average Error: 0.2 → 0.2
Time: 17.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r28117 = x;
        double r28118 = 1.0;
        double r28119 = B;
        double r28120 = tan(r28119);
        double r28121 = r28118 / r28120;
        double r28122 = r28117 * r28121;
        double r28123 = -r28122;
        double r28124 = sin(r28119);
        double r28125 = r28118 / r28124;
        double r28126 = r28123 + r28125;
        return r28126;
}
↓
double f(double B, double x) {
        double r28127 = 1.0;
        double r28128 = x;
        double r28129 = B;
        double r28130 = cos(r28129);
        double r28131 = r28128 * r28130;
        double r28132 = sin(r28129);
        double r28133 = r28131 / r28132;
        double r28134 = r28127 * r28133;
        double r28135 = -r28134;
        double r28136 = r28127 / r28132;
        double r28137 = r28135 + r28136;
        return r28137;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))