Average Error: 0.2 → 0.2
Time: 25.8s
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 r25361 = x;
        double r25362 = 1.0;
        double r25363 = B;
        double r25364 = tan(r25363);
        double r25365 = r25362 / r25364;
        double r25366 = r25361 * r25365;
        double r25367 = -r25366;
        double r25368 = sin(r25363);
        double r25369 = r25362 / r25368;
        double r25370 = r25367 + r25369;
        return r25370;
}
↓
double f(double B, double x) {
        double r25371 = 1.0;
        double r25372 = 1.0;
        double r25373 = B;
        double r25374 = sin(r25373);
        double r25375 = r25372 / r25374;
        double r25376 = x;
        double r25377 = cos(r25373);
        double r25378 = r25376 * r25377;
        double r25379 = r25378 / r25374;
        double r25380 = r25375 - r25379;
        double r25381 = r25371 * r25380;
        return r25381;
}

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. Taylor expanded around inf 0.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))