Average Error: 0.2 → 0.2
Time: 23.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22570 = x;
        double r22571 = 1.0;
        double r22572 = B;
        double r22573 = tan(r22572);
        double r22574 = r22571 / r22573;
        double r22575 = r22570 * r22574;
        double r22576 = -r22575;
        double r22577 = sin(r22572);
        double r22578 = r22571 / r22577;
        double r22579 = r22576 + r22578;
        return r22579;
}
↓
double f(double B, double x) {
        double r22580 = 1.0;
        double r22581 = x;
        double r22582 = B;
        double r22583 = sin(r22582);
        double r22584 = r22581 / r22583;
        double r22585 = r22580 * r22584;
        double r22586 = cos(r22582);
        double r22587 = r22585 * r22586;
        double r22588 = -r22587;
        double r22589 = r22580 / r22583;
        double r22590 = r22588 + r22589;
        return r22590;
}

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 tan-quot0.2

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

  4. Applied associate-/r/0.3

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

  5. Applied associate-*r*0.3

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

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