Average Error: 0.2 → 0.2
Time: 23.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22594 = x;
        double r22595 = 1.0;
        double r22596 = B;
        double r22597 = tan(r22596);
        double r22598 = r22595 / r22597;
        double r22599 = r22594 * r22598;
        double r22600 = -r22599;
        double r22601 = sin(r22596);
        double r22602 = r22595 / r22601;
        double r22603 = r22600 + r22602;
        return r22603;
}
↓
double f(double B, double x) {
        double r22604 = x;
        double r22605 = 1.0;
        double r22606 = r22604 * r22605;
        double r22607 = B;
        double r22608 = sin(r22607);
        double r22609 = r22606 / r22608;
        double r22610 = cos(r22607);
        double r22611 = r22609 * r22610;
        double r22612 = -r22611;
        double r22613 = r22605 / r22608;
        double r22614 = r22612 + r22613;
        return r22614;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))