Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t) {
        double r101057 = x;
        double r101058 = y;
        double r101059 = log(r101058);
        double r101060 = r101057 * r101059;
        double r101061 = r101060 - r101058;
        double r101062 = z;
        double r101063 = r101061 - r101062;
        double r101064 = t;
        double r101065 = log(r101064);
        double r101066 = r101063 + r101065;
        return r101066;
}
↓
double f(double x, double y, double z, double t) {
        double r101067 = x;
        double r101068 = y;
        double r101069 = log(r101068);
        double r101070 = r101067 * r101069;
        double r101071 = r101070 - r101068;
        double r101072 = z;
        double r101073 = r101071 - r101072;
        double r101074 = t;
        double r101075 = sqrt(r101074);
        double r101076 = log(r101075);
        double r101077 = r101073 + r101076;
        double r101078 = r101077 + r101076;
        return r101078;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))