Average Error: 0.2 → 0.2
Time: 21.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r2100442 = x;
        double r2100443 = 1.0;
        double r2100444 = B;
        double r2100445 = tan(r2100444);
        double r2100446 = r2100443 / r2100445;
        double r2100447 = r2100442 * r2100446;
        double r2100448 = -r2100447;
        double r2100449 = sin(r2100444);
        double r2100450 = r2100443 / r2100449;
        double r2100451 = r2100448 + r2100450;
        return r2100451;
}
↓
double f(double B, double x) {
        double r2100452 = 1.0;
        double r2100453 = B;
        double r2100454 = sin(r2100453);
        double r2100455 = r2100452 / r2100454;
        double r2100456 = x;
        double r2100457 = r2100456 / r2100454;
        double r2100458 = cos(r2100453);
        double r2100459 = r2100457 * r2100458;
        double r2100460 = r2100455 - r2100459;
        return r2100460;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))