Average Error: 0.2 → 0.2
Time: 24.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r367489 = x;
        double r367490 = 1.0;
        double r367491 = B;
        double r367492 = tan(r367491);
        double r367493 = r367490 / r367492;
        double r367494 = r367489 * r367493;
        double r367495 = -r367494;
        double r367496 = sin(r367491);
        double r367497 = r367490 / r367496;
        double r367498 = r367495 + r367497;
        return r367498;
}
↓
double f(double B, double x) {
        double r367499 = 1.0;
        double r367500 = B;
        double r367501 = cos(r367500);
        double r367502 = x;
        double r367503 = r367501 * r367502;
        double r367504 = r367499 - r367503;
        double r367505 = sin(r367500);
        double r367506 = r367504 / r367505;
        return r367506;
}

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

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

  3. Taylor expanded around -inf 0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))