Average Error: 0.2 → 0.2
Time: 20.6s
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 r1814759 = x;
        double r1814760 = 1.0;
        double r1814761 = B;
        double r1814762 = tan(r1814761);
        double r1814763 = r1814760 / r1814762;
        double r1814764 = r1814759 * r1814763;
        double r1814765 = -r1814764;
        double r1814766 = sin(r1814761);
        double r1814767 = r1814760 / r1814766;
        double r1814768 = r1814765 + r1814767;
        return r1814768;
}
↓
double f(double B, double x) {
        double r1814769 = 1.0;
        double r1814770 = B;
        double r1814771 = cos(r1814770);
        double r1814772 = x;
        double r1814773 = r1814771 * r1814772;
        double r1814774 = r1814769 - r1814773;
        double r1814775 = sin(r1814770);
        double r1814776 = r1814774 / r1814775;
        return r1814776;
}

Error

Bits error versus B

Bits error versus x

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Your Program's Arguments

Results

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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. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  7. Applied associate-*l/0.2

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

  8. Applied sub-div0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019129 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))