Average Error: 0.2 → 0.2
Time: 1.7m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r495784 = x;
        double r495785 = 1.0;
        double r495786 = B;
        double r495787 = tan(r495786);
        double r495788 = r495785 / r495787;
        double r495789 = r495784 * r495788;
        double r495790 = -r495789;
        double r495791 = sin(r495786);
        double r495792 = r495785 / r495791;
        double r495793 = r495790 + r495792;
        return r495793;
}
↓
double f(double B, double x) {
        double r495794 = 1.0;
        double r495795 = B;
        double r495796 = sin(r495795);
        double r495797 = r495794 / r495796;
        double r495798 = x;
        double r495799 = r495798 / r495796;
        double r495800 = cos(r495795);
        double r495801 = r495799 * r495800;
        double r495802 = r495797 - r495801;
        return r495802;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019143 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))