Average Error: 0.2 → 0.3
Time: 5.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \left(\left(x \cdot \cos B\right) \cdot \frac{1}{\sin B}\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \left(\left(x \cdot \cos B\right) \cdot \frac{1}{\sin B}\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r14032 = x;
        double r14033 = 1.0;
        double r14034 = B;
        double r14035 = tan(r14034);
        double r14036 = r14033 / r14035;
        double r14037 = r14032 * r14036;
        double r14038 = -r14037;
        double r14039 = sin(r14034);
        double r14040 = r14033 / r14039;
        double r14041 = r14038 + r14040;
        return r14041;
}
↓
double f(double B, double x) {
        double r14042 = 1.0;
        double r14043 = x;
        double r14044 = B;
        double r14045 = cos(r14044);
        double r14046 = r14043 * r14045;
        double r14047 = 1.0;
        double r14048 = sin(r14044);
        double r14049 = r14047 / r14048;
        double r14050 = r14046 * r14049;
        double r14051 = r14042 * r14050;
        double r14052 = -r14051;
        double r14053 = r14042 / r14048;
        double r14054 = r14052 + r14053;
        return r14054;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Taylor expanded around inf 0.2

    \[\leadsto \left(-\color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\right) + \frac{1}{\sin B}\]
  3. Using strategy rm

  4. Applied div-inv0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))