Average Error: 0.1 → 0.1
Time: 12.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log t - z\right) + \left(2 \cdot \log \left(\sqrt[3]{y}\right) - \log y \cdot \frac{-1}{3}\right) \cdot x\right) - y\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log t - z\right) + \left(2 \cdot \log \left(\sqrt[3]{y}\right) - \log y \cdot \frac{-1}{3}\right) \cdot x\right) - y
double f(double x, double y, double z, double t) {
        double r96980 = x;
        double r96981 = y;
        double r96982 = log(r96981);
        double r96983 = r96980 * r96982;
        double r96984 = r96983 - r96981;
        double r96985 = z;
        double r96986 = r96984 - r96985;
        double r96987 = t;
        double r96988 = log(r96987);
        double r96989 = r96986 + r96988;
        return r96989;
}
↓
double f(double x, double y, double z, double t) {
        double r96990 = t;
        double r96991 = log(r96990);
        double r96992 = z;
        double r96993 = r96991 - r96992;
        double r96994 = 2.0;
        double r96995 = y;
        double r96996 = cbrt(r96995);
        double r96997 = log(r96996);
        double r96998 = r96994 * r96997;
        double r96999 = log(r96995);
        double r97000 = -0.3333333333333333;
        double r97001 = r96999 * r97000;
        double r97002 = r96998 - r97001;
        double r97003 = x;
        double r97004 = r97002 * r97003;
        double r97005 = r96993 + r97004;
        double r97006 = r97005 - r96995;
        return r97006;
}

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. Taylor expanded around inf 0.1

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

  10. Final simplification0.1

    \[\leadsto \left(\left(\log t - z\right) + \left(2 \cdot \log \left(\sqrt[3]{y}\right) - \log y \cdot \frac{-1}{3}\right) \cdot x\right) - y\]

Reproduce

herbie shell --seed 1978988140 
(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)))