Average Error: 0.2 → 0.2
Time: 15.9s
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 r23191 = x;
        double r23192 = 1.0;
        double r23193 = B;
        double r23194 = tan(r23193);
        double r23195 = r23192 / r23194;
        double r23196 = r23191 * r23195;
        double r23197 = -r23196;
        double r23198 = sin(r23193);
        double r23199 = r23192 / r23198;
        double r23200 = r23197 + r23199;
        return r23200;
}
↓
double f(double B, double x) {
        double r23201 = x;
        double r23202 = 1.0;
        double r23203 = r23201 * r23202;
        double r23204 = B;
        double r23205 = sin(r23204);
        double r23206 = r23203 / r23205;
        double r23207 = cos(r23204);
        double r23208 = r23206 * r23207;
        double r23209 = -r23208;
        double r23210 = r23202 / r23205;
        double r23211 = r23209 + r23210;
        return r23211;
}

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/0.1

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  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 2019208 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))