Average Error: 0.1 → 0.1
Time: 19.7s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[2 \cdot \log \left(\sqrt{t}\right) + \left(\left(x \cdot \log y - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
2 \cdot \log \left(\sqrt{t}\right) + \left(\left(x \cdot \log y - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r104101 = x;
        double r104102 = y;
        double r104103 = log(r104102);
        double r104104 = r104101 * r104103;
        double r104105 = r104104 - r104102;
        double r104106 = z;
        double r104107 = r104105 - r104106;
        double r104108 = t;
        double r104109 = log(r104108);
        double r104110 = r104107 + r104109;
        return r104110;
}
↓
double f(double x, double y, double z, double t) {
        double r104111 = 2.0;
        double r104112 = t;
        double r104113 = sqrt(r104112);
        double r104114 = log(r104113);
        double r104115 = r104111 * r104114;
        double r104116 = x;
        double r104117 = y;
        double r104118 = log(r104117);
        double r104119 = r104116 * r104118;
        double r104120 = r104119 - r104117;
        double r104121 = z;
        double r104122 = r104120 - r104121;
        double r104123 = r104115 + r104122;
        return r104123;
}

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

    \[\leadsto 2 \cdot \log \left(\sqrt{t}\right) + \left(\left(x \cdot \log y - y\right) - z\right)\]

Reproduce

herbie shell --seed 2019291 
(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)))