Average Error: 0.2 → 0.2
Time: 7.4m
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 r8009302 = x;
        double r8009303 = 1.0;
        double r8009304 = B;
        double r8009305 = tan(r8009304);
        double r8009306 = r8009303 / r8009305;
        double r8009307 = r8009302 * r8009306;
        double r8009308 = -r8009307;
        double r8009309 = sin(r8009304);
        double r8009310 = r8009303 / r8009309;
        double r8009311 = r8009308 + r8009310;
        return r8009311;
}
↓
double f(double B, double x) {
        double r8009312 = 1.0;
        double r8009313 = B;
        double r8009314 = cos(r8009313);
        double r8009315 = x;
        double r8009316 = r8009314 * r8009315;
        double r8009317 = r8009312 - r8009316;
        double r8009318 = sin(r8009313);
        double r8009319 = r8009317 / r8009318;
        return r8009319;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019128 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))