Average Error: 0.1 → 0.1
Time: 24.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right)
double f(double x, double y, double z, double t) {
        double r4854654 = x;
        double r4854655 = y;
        double r4854656 = log(r4854655);
        double r4854657 = r4854654 * r4854656;
        double r4854658 = r4854657 - r4854655;
        double r4854659 = z;
        double r4854660 = r4854658 - r4854659;
        double r4854661 = t;
        double r4854662 = log(r4854661);
        double r4854663 = r4854660 + r4854662;
        return r4854663;
}
↓
double f(double x, double y, double z, double t) {
        double r4854664 = t;
        double r4854665 = log(r4854664);
        double r4854666 = y;
        double r4854667 = cbrt(r4854666);
        double r4854668 = log(r4854667);
        double r4854669 = x;
        double r4854670 = r4854668 * r4854669;
        double r4854671 = r4854670 - r4854666;
        double r4854672 = z;
        double r4854673 = r4854671 - r4854672;
        double r4854674 = r4854667 * r4854667;
        double r4854675 = log(r4854674);
        double r4854676 = r4854675 * r4854669;
        double r4854677 = r4854673 + r4854676;
        double r4854678 = r4854665 + r4854677;
        return r4854678;
}

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. Applied associate--l+0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))