Average Error: 0.1 → 0.1
Time: 7.6s
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 r80076 = x;
        double r80077 = y;
        double r80078 = log(r80077);
        double r80079 = r80076 * r80078;
        double r80080 = r80079 - r80077;
        double r80081 = z;
        double r80082 = r80080 - r80081;
        double r80083 = t;
        double r80084 = log(r80083);
        double r80085 = r80082 + r80084;
        return r80085;
}
↓
double f(double x, double y, double z, double t) {
        double r80086 = x;
        double r80087 = y;
        double r80088 = log(r80087);
        double r80089 = r80086 * r80088;
        double r80090 = r80089 - r80087;
        double r80091 = z;
        double r80092 = r80090 - r80091;
        double r80093 = t;
        double r80094 = sqrt(r80093);
        double r80095 = log(r80094);
        double r80096 = r80092 + r80095;
        double r80097 = r80096 + r80095;
        return r80097;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. 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 2020002 
(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)))