Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x}{\frac{\sin B}{\cos B}}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x}{\frac{\sin B}{\cos B}}\right)
double f(double B, double x) {
        double r52340 = x;
        double r52341 = 1.0;
        double r52342 = B;
        double r52343 = tan(r52342);
        double r52344 = r52341 / r52343;
        double r52345 = r52340 * r52344;
        double r52346 = -r52345;
        double r52347 = sin(r52342);
        double r52348 = r52341 / r52347;
        double r52349 = r52346 + r52348;
        return r52349;
}
↓
double f(double B, double x) {
        double r52350 = 1.0;
        double r52351 = 1.0;
        double r52352 = B;
        double r52353 = sin(r52352);
        double r52354 = r52351 / r52353;
        double r52355 = x;
        double r52356 = cos(r52352);
        double r52357 = r52353 / r52356;
        double r52358 = r52355 / r52357;
        double r52359 = r52354 - r52358;
        double r52360 = r52350 * r52359;
        return r52360;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]

  3. Taylor expanded around inf 0.2

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

  4. Simplified0.2

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

  6. Applied associate-/l*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))