Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r15682 = x;
        double r15683 = 1.0;
        double r15684 = B;
        double r15685 = tan(r15684);
        double r15686 = r15683 / r15685;
        double r15687 = r15682 * r15686;
        double r15688 = -r15687;
        double r15689 = sin(r15684);
        double r15690 = r15683 / r15689;
        double r15691 = r15688 + r15690;
        return r15691;
}
↓
double f(double B, double x) {
        double r15692 = 1.0;
        double r15693 = B;
        double r15694 = sin(r15693);
        double r15695 = r15692 / r15694;
        double r15696 = x;
        double r15697 = cos(r15693);
        double r15698 = r15696 * r15697;
        double r15699 = r15698 / r15694;
        double r15700 = r15692 * r15699;
        double r15701 = r15695 - r15700;
        return r15701;
}

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

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

  4. Applied associate-*r/0.2

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

  5. Taylor expanded around inf 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))