Average Error: 0.2 → 0.2
Time: 19.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r23355 = x;
        double r23356 = 1.0;
        double r23357 = B;
        double r23358 = tan(r23357);
        double r23359 = r23356 / r23358;
        double r23360 = r23355 * r23359;
        double r23361 = -r23360;
        double r23362 = sin(r23357);
        double r23363 = r23356 / r23362;
        double r23364 = r23361 + r23363;
        return r23364;
}
↓
double f(double B, double x) {
        double r23365 = x;
        double r23366 = 1.0;
        double r23367 = B;
        double r23368 = cos(r23367);
        double r23369 = sin(r23367);
        double r23370 = r23368 / r23369;
        double r23371 = r23366 * r23370;
        double r23372 = r23365 * r23371;
        double r23373 = -r23372;
        double r23374 = r23366 / r23369;
        double r23375 = r23373 + r23374;
        return r23375;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))