Average Error: 0.2 → 0.2
Time: 4.5s
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 r10066 = x;
        double r10067 = 1.0;
        double r10068 = B;
        double r10069 = tan(r10068);
        double r10070 = r10067 / r10069;
        double r10071 = r10066 * r10070;
        double r10072 = -r10071;
        double r10073 = sin(r10068);
        double r10074 = r10067 / r10073;
        double r10075 = r10072 + r10074;
        return r10075;
}
↓
double f(double B, double x) {
        double r10076 = x;
        double r10077 = 1.0;
        double r10078 = r10076 * r10077;
        double r10079 = B;
        double r10080 = sin(r10079);
        double r10081 = r10078 / r10080;
        double r10082 = cos(r10079);
        double r10083 = r10081 * r10082;
        double r10084 = -r10083;
        double r10085 = r10077 / r10080;
        double r10086 = r10084 + r10085;
        return r10086;
}

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 2020062 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))