Average Error: 0.2 → 0.2
Time: 5.3s
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 r42190 = x;
        double r42191 = 1.0;
        double r42192 = B;
        double r42193 = tan(r42192);
        double r42194 = r42191 / r42193;
        double r42195 = r42190 * r42194;
        double r42196 = -r42195;
        double r42197 = sin(r42192);
        double r42198 = r42191 / r42197;
        double r42199 = r42196 + r42198;
        return r42199;
}
↓
double f(double B, double x) {
        double r42200 = 1.0;
        double r42201 = 1.0;
        double r42202 = B;
        double r42203 = sin(r42202);
        double r42204 = r42201 / r42203;
        double r42205 = x;
        double r42206 = cos(r42202);
        double r42207 = r42205 * r42206;
        double r42208 = r42207 / r42203;
        double r42209 = r42204 - r42208;
        double r42210 = r42200 * r42209;
        return r42210;
}

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 associate-*r/0.1

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

  5. Taylor expanded around inf 0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019356 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))