Average Error: 0.2 → 0.2
Time: 11.7s
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 r64430 = x;
        double r64431 = 1.0;
        double r64432 = B;
        double r64433 = tan(r64432);
        double r64434 = r64431 / r64433;
        double r64435 = r64430 * r64434;
        double r64436 = -r64435;
        double r64437 = sin(r64432);
        double r64438 = r64431 / r64437;
        double r64439 = r64436 + r64438;
        return r64439;
}
↓
double f(double B, double x) {
        double r64440 = x;
        double r64441 = 1.0;
        double r64442 = r64440 * r64441;
        double r64443 = B;
        double r64444 = sin(r64443);
        double r64445 = r64442 / r64444;
        double r64446 = cos(r64443);
        double r64447 = r64445 * r64446;
        double r64448 = -r64447;
        double r64449 = r64441 / r64444;
        double r64450 = r64448 + r64449;
        return r64450;
}

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/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  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 2019351 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))