Average Error: 0.1 → 0.1
Time: 24.7s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot x\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot x\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r131677 = x;
        double r131678 = y;
        double r131679 = log(r131678);
        double r131680 = r131677 * r131679;
        double r131681 = r131680 - r131678;
        double r131682 = z;
        double r131683 = r131681 - r131682;
        double r131684 = t;
        double r131685 = log(r131684);
        double r131686 = r131683 + r131685;
        return r131686;
}
↓
double f(double x, double y, double z, double t) {
        double r131687 = 2.0;
        double r131688 = y;
        double r131689 = cbrt(r131688);
        double r131690 = log(r131689);
        double r131691 = r131687 * r131690;
        double r131692 = x;
        double r131693 = r131691 * r131692;
        double r131694 = 1.0;
        double r131695 = r131694 / r131688;
        double r131696 = -0.3333333333333333;
        double r131697 = pow(r131695, r131696);
        double r131698 = log(r131697);
        double r131699 = r131698 * r131692;
        double r131700 = r131693 + r131699;
        double r131701 = r131700 - r131688;
        double r131702 = z;
        double r131703 = r131701 - r131702;
        double r131704 = t;
        double r131705 = log(r131704);
        double r131706 = r131703 + r131705;
        return r131706;
}

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. Simplified0.1

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

  7. Simplified0.1

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

  8. Taylor expanded around inf 0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(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)))