Average Error: 0.1 → 0.1
Time: 25.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r81352 = x;
        double r81353 = y;
        double r81354 = log(r81353);
        double r81355 = r81352 * r81354;
        double r81356 = r81355 - r81353;
        double r81357 = z;
        double r81358 = r81356 - r81357;
        double r81359 = t;
        double r81360 = log(r81359);
        double r81361 = r81358 + r81360;
        return r81361;
}
↓
double f(double x, double y, double z, double t) {
        double r81362 = y;
        double r81363 = cbrt(r81362);
        double r81364 = r81363 * r81363;
        double r81365 = log(r81364);
        double r81366 = x;
        double r81367 = r81365 * r81366;
        double r81368 = log(r81363);
        double r81369 = r81368 * r81366;
        double r81370 = r81369 - r81362;
        double r81371 = r81367 + r81370;
        double r81372 = z;
        double r81373 = r81371 - r81372;
        double r81374 = t;
        double r81375 = log(r81374);
        double r81376 = r81373 + r81375;
        return r81376;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - z\right) + \log t\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} - y\right) - z\right) + \log t\]

  6. Applied associate--l+0.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right)} - z\right) + \log t\]

  7. Final simplification0.1

    \[\leadsto \left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))