Average Error: 0.2 → 0.2
Time: 22.1s
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 r398080 = x;
        double r398081 = 1.0;
        double r398082 = B;
        double r398083 = tan(r398082);
        double r398084 = r398081 / r398083;
        double r398085 = r398080 * r398084;
        double r398086 = -r398085;
        double r398087 = sin(r398082);
        double r398088 = r398081 / r398087;
        double r398089 = r398086 + r398088;
        return r398089;
}
↓
double f(double B, double x) {
        double r398090 = 1.0;
        double r398091 = B;
        double r398092 = sin(r398091);
        double r398093 = r398090 / r398092;
        double r398094 = x;
        double r398095 = r398094 / r398092;
        double r398096 = cos(r398091);
        double r398097 = r398095 * r398096;
        double r398098 = r398093 - r398097;
        return r398098;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019138 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))