Average Error: 0.2 → 0.6
Time: 30.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{\cos B}{\sqrt[3]{\sin B}} \cdot \frac{x \cdot 1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{\cos B}{\sqrt[3]{\sin B}} \cdot \frac{x \cdot 1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}
double f(double B, double x) {
        double r977522 = x;
        double r977523 = 1.0;
        double r977524 = B;
        double r977525 = tan(r977524);
        double r977526 = r977523 / r977525;
        double r977527 = r977522 * r977526;
        double r977528 = -r977527;
        double r977529 = sin(r977524);
        double r977530 = r977523 / r977529;
        double r977531 = r977528 + r977530;
        return r977531;
}
↓
double f(double B, double x) {
        double r977532 = 1.0;
        double r977533 = B;
        double r977534 = sin(r977533);
        double r977535 = r977532 / r977534;
        double r977536 = cos(r977533);
        double r977537 = cbrt(r977534);
        double r977538 = r977536 / r977537;
        double r977539 = x;
        double r977540 = r977539 * r977532;
        double r977541 = r977537 * r977537;
        double r977542 = r977540 / r977541;
        double r977543 = r977538 * r977542;
        double r977544 = r977535 - r977543;
        return r977544;
}

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. Simplified0.1

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

  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

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

  6. Applied add-cube-cbrt0.6

    \[\leadsto \frac{1}{\sin B} - \frac{\left(1 \cdot x\right) \cdot \cos B}{\color{blue}{\left(\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}\right) \cdot \sqrt[3]{\sin B}}}\]

  7. Applied times-frac0.6

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{1 \cdot x}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}} \cdot \frac{\cos B}{\sqrt[3]{\sin B}}}\]

  8. Final simplification0.6

    \[\leadsto \frac{1}{\sin B} - \frac{\cos B}{\sqrt[3]{\sin B}} \cdot \frac{x \cdot 1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))