Average Error: 0.1 → 0.1
Time: 27.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r5302003 = x;
        double r5302004 = y;
        double r5302005 = log(r5302004);
        double r5302006 = r5302003 * r5302005;
        double r5302007 = r5302006 - r5302004;
        double r5302008 = z;
        double r5302009 = r5302007 - r5302008;
        double r5302010 = t;
        double r5302011 = log(r5302010);
        double r5302012 = r5302009 + r5302011;
        return r5302012;
}
↓
double f(double x, double y, double z, double t) {
        double r5302013 = t;
        double r5302014 = log(r5302013);
        double r5302015 = y;
        double r5302016 = cbrt(r5302015);
        double r5302017 = r5302016 * r5302016;
        double r5302018 = log(r5302017);
        double r5302019 = x;
        double r5302020 = r5302018 * r5302019;
        double r5302021 = 0.3333333333333333;
        double r5302022 = pow(r5302015, r5302021);
        double r5302023 = log(r5302022);
        double r5302024 = r5302019 * r5302023;
        double r5302025 = r5302020 + r5302024;
        double r5302026 = r5302025 - r5302015;
        double r5302027 = z;
        double r5302028 = r5302026 - r5302027;
        double r5302029 = r5302014 + r5302028;
        return r5302029;
}

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. Using strategy rm

  7. Applied pow1/30.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))