Average Error: 0.2 → 0.2
Time: 20.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}
double f(double B, double x) {
        double r817044 = x;
        double r817045 = 1.0;
        double r817046 = B;
        double r817047 = tan(r817046);
        double r817048 = r817045 / r817047;
        double r817049 = r817044 * r817048;
        double r817050 = -r817049;
        double r817051 = sin(r817046);
        double r817052 = r817045 / r817051;
        double r817053 = r817050 + r817052;
        return r817053;
}
↓
double f(double B, double x) {
        double r817054 = 1.0;
        double r817055 = B;
        double r817056 = cos(r817055);
        double r817057 = x;
        double r817058 = r817054 * r817057;
        double r817059 = r817056 * r817058;
        double r817060 = r817054 - r817059;
        double r817061 = sin(r817055);
        double r817062 = r817060 / r817061;
        return r817062;
}

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

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  7. Applied associate-*l/0.2

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

  8. Applied sub-div0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))