Average Error: 0.1 → 0.1
Time: 28.3s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(x \cdot \log \left({y}^{\frac{1}{3}}\right) - y\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(x \cdot \log \left({y}^{\frac{1}{3}}\right) - y\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) - z\right)
double f(double x, double y, double z, double t) {
        double r6222681 = x;
        double r6222682 = y;
        double r6222683 = log(r6222682);
        double r6222684 = r6222681 * r6222683;
        double r6222685 = r6222684 - r6222682;
        double r6222686 = z;
        double r6222687 = r6222685 - r6222686;
        double r6222688 = t;
        double r6222689 = log(r6222688);
        double r6222690 = r6222687 + r6222689;
        return r6222690;
}
↓
double f(double x, double y, double z, double t) {
        double r6222691 = t;
        double r6222692 = log(r6222691);
        double r6222693 = x;
        double r6222694 = y;
        double r6222695 = 0.3333333333333333;
        double r6222696 = pow(r6222694, r6222695);
        double r6222697 = log(r6222696);
        double r6222698 = r6222693 * r6222697;
        double r6222699 = r6222698 - r6222694;
        double r6222700 = cbrt(r6222694);
        double r6222701 = r6222700 * r6222700;
        double r6222702 = log(r6222701);
        double r6222703 = r6222702 * r6222693;
        double r6222704 = r6222699 + r6222703;
        double r6222705 = z;
        double r6222706 = r6222704 - r6222705;
        double r6222707 = r6222692 + r6222706;
        return r6222707;
}

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. Using strategy rm

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))