Average Error: 0.2 → 0.2
Time: 35.9s
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 r1902557 = x;
        double r1902558 = 1.0;
        double r1902559 = B;
        double r1902560 = tan(r1902559);
        double r1902561 = r1902558 / r1902560;
        double r1902562 = r1902557 * r1902561;
        double r1902563 = -r1902562;
        double r1902564 = sin(r1902559);
        double r1902565 = r1902558 / r1902564;
        double r1902566 = r1902563 + r1902565;
        return r1902566;
}
↓
double f(double B, double x) {
        double r1902567 = 1.0;
        double r1902568 = B;
        double r1902569 = cos(r1902568);
        double r1902570 = x;
        double r1902571 = r1902569 * r1902570;
        double r1902572 = r1902567 - r1902571;
        double r1902573 = sin(r1902568);
        double r1902574 = r1902572 / r1902573;
        return r1902574;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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. 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 2019121 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))