Average Error: 0.2 → 0.2
Time: 24.7s
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 r2100606 = x;
        double r2100607 = 1.0;
        double r2100608 = B;
        double r2100609 = tan(r2100608);
        double r2100610 = r2100607 / r2100609;
        double r2100611 = r2100606 * r2100610;
        double r2100612 = -r2100611;
        double r2100613 = sin(r2100608);
        double r2100614 = r2100607 / r2100613;
        double r2100615 = r2100612 + r2100614;
        return r2100615;
}
↓
double f(double B, double x) {
        double r2100616 = 1.0;
        double r2100617 = B;
        double r2100618 = cos(r2100617);
        double r2100619 = x;
        double r2100620 = r2100618 * r2100619;
        double r2100621 = r2100616 - r2100620;
        double r2100622 = sin(r2100617);
        double r2100623 = r2100621 / r2100622;
        return r2100623;
}

Error

Bits error versus B

Bits error versus x

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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. 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 2019134 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))