Average Error: 0.1 → 0.1
Time: 9.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right)\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right)\right) + \log t
double f(double x, double y, double z, double t) {
        double r129364 = x;
        double r129365 = y;
        double r129366 = log(r129365);
        double r129367 = r129364 * r129366;
        double r129368 = r129367 - r129365;
        double r129369 = z;
        double r129370 = r129368 - r129369;
        double r129371 = t;
        double r129372 = log(r129371);
        double r129373 = r129370 + r129372;
        return r129373;
}
↓
double f(double x, double y, double z, double t) {
        double r129374 = x;
        double r129375 = y;
        double r129376 = cbrt(r129375);
        double r129377 = r129376 * r129376;
        double r129378 = log(r129377);
        double r129379 = r129374 * r129378;
        double r129380 = 0.3333333333333333;
        double r129381 = pow(r129375, r129380);
        double r129382 = log(r129381);
        double r129383 = r129382 * r129374;
        double r129384 = r129383 - r129375;
        double r129385 = z;
        double r129386 = r129384 - r129385;
        double r129387 = r129379 + r129386;
        double r129388 = t;
        double r129389 = log(r129388);
        double r129390 = r129387 + r129389;
        return r129390;
}

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-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Simplified0.1

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

  10. Applied pow1/30.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \color{blue}{\left({y}^{\frac{1}{3}}\right)} \cdot x - y\right) - z\right)\right) + \log t\]

  11. Final simplification0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right)\right) + \log t\]

Reproduce

herbie shell --seed 2019322 
(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)))