Average Error: 0.1 → 0.1
Time: 6.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\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
double f(double x, double y, double z, double t) {
        double r123236 = x;
        double r123237 = y;
        double r123238 = log(r123237);
        double r123239 = r123236 * r123238;
        double r123240 = r123239 - r123237;
        double r123241 = z;
        double r123242 = r123240 - r123241;
        double r123243 = t;
        double r123244 = log(r123243);
        double r123245 = r123242 + r123244;
        return r123245;
}
↓
double f(double x, double y, double z, double t) {
        double r123246 = y;
        double r123247 = cbrt(r123246);
        double r123248 = r123247 * r123247;
        double r123249 = log(r123248);
        double r123250 = x;
        double r123251 = r123249 * r123250;
        double r123252 = log(r123247);
        double r123253 = r123252 * r123250;
        double r123254 = r123253 - r123246;
        double r123255 = z;
        double r123256 = r123254 - r123255;
        double r123257 = r123251 + r123256;
        double r123258 = t;
        double r123259 = log(r123258);
        double r123260 = r123257 + r123259;
        return r123260;
}

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

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

Reproduce

herbie shell --seed 2020060 
(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)))