Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt{t}\right) + \log y \cdot x\right) - \left(y + z\right)\right) + \log \left(\sqrt{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt{t}\right) + \log y \cdot x\right) - \left(y + z\right)\right) + \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t) {
        double r99056 = x;
        double r99057 = y;
        double r99058 = log(r99057);
        double r99059 = r99056 * r99058;
        double r99060 = r99059 - r99057;
        double r99061 = z;
        double r99062 = r99060 - r99061;
        double r99063 = t;
        double r99064 = log(r99063);
        double r99065 = r99062 + r99064;
        return r99065;
}
↓
double f(double x, double y, double z, double t) {
        double r99066 = t;
        double r99067 = sqrt(r99066);
        double r99068 = log(r99067);
        double r99069 = y;
        double r99070 = log(r99069);
        double r99071 = x;
        double r99072 = r99070 * r99071;
        double r99073 = r99068 + r99072;
        double r99074 = z;
        double r99075 = r99069 + r99074;
        double r99076 = r99073 - r99075;
        double r99077 = r99076 + r99068;
        return r99077;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))