Average Error: 0.1 → 0.1
Time: 6.7s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r85114 = x;
        double r85115 = y;
        double r85116 = log(r85115);
        double r85117 = r85114 * r85116;
        double r85118 = r85117 - r85115;
        double r85119 = z;
        double r85120 = r85118 - r85119;
        double r85121 = t;
        double r85122 = log(r85121);
        double r85123 = r85120 + r85122;
        return r85123;
}
↓
double f(double x, double y, double z, double t) {
        double r85124 = 1.0;
        double r85125 = y;
        double r85126 = r85124 / r85125;
        double r85127 = -0.3333333333333333;
        double r85128 = pow(r85126, r85127);
        double r85129 = cbrt(r85125);
        double r85130 = r85128 * r85129;
        double r85131 = log(r85130);
        double r85132 = x;
        double r85133 = r85131 * r85132;
        double r85134 = log(r85129);
        double r85135 = r85134 * r85132;
        double r85136 = r85135 - r85125;
        double r85137 = r85133 + r85136;
        double r85138 = z;
        double r85139 = r85137 - r85138;
        double r85140 = t;
        double r85141 = log(r85140);
        double r85142 = r85139 + r85141;
        return r85142;
}

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. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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)))