Average Error: 0.2 → 0.2
Time: 28.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r1506215 = x;
        double r1506216 = 1.0;
        double r1506217 = B;
        double r1506218 = tan(r1506217);
        double r1506219 = r1506216 / r1506218;
        double r1506220 = r1506215 * r1506219;
        double r1506221 = -r1506220;
        double r1506222 = sin(r1506217);
        double r1506223 = r1506216 / r1506222;
        double r1506224 = r1506221 + r1506223;
        return r1506224;
}
↓
double f(double B, double x) {
        double r1506225 = 1.0;
        double r1506226 = B;
        double r1506227 = sin(r1506226);
        double r1506228 = r1506225 / r1506227;
        double r1506229 = x;
        double r1506230 = cos(r1506226);
        double r1506231 = r1506229 * r1506230;
        double r1506232 = r1506231 / r1506227;
        double r1506233 = r1506228 - r1506232;
        return r1506233;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))