Average Error: 0.2 → 0.7
Time: 22.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\tan B} \cdot \sqrt[3]{\tan B}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\tan B}}\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\tan B} \cdot \sqrt[3]{\tan B}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\tan B}}\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r47377 = x;
        double r47378 = 1.0;
        double r47379 = B;
        double r47380 = tan(r47379);
        double r47381 = r47378 / r47380;
        double r47382 = r47377 * r47381;
        double r47383 = -r47382;
        double r47384 = sin(r47379);
        double r47385 = r47378 / r47384;
        double r47386 = r47383 + r47385;
        return r47386;
}
↓
double f(double B, double x) {
        double r47387 = x;
        double r47388 = 1.0;
        double r47389 = cbrt(r47388);
        double r47390 = r47389 * r47389;
        double r47391 = B;
        double r47392 = tan(r47391);
        double r47393 = cbrt(r47392);
        double r47394 = r47393 * r47393;
        double r47395 = r47390 / r47394;
        double r47396 = r47389 / r47393;
        double r47397 = r47395 * r47396;
        double r47398 = r47387 * r47397;
        double r47399 = -r47398;
        double r47400 = sin(r47391);
        double r47401 = r47388 / r47400;
        double r47402 = r47399 + r47401;
        return r47402;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.7

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

  4. Applied add-cube-cbrt0.7

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

  5. Applied times-frac0.7

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

  6. Final simplification0.7

    \[\leadsto \left(-x \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\tan B} \cdot \sqrt[3]{\tan B}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\tan B}}\right)\right) + \frac{1}{\sin B}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))