Average Error: 0.2 → 0.3
Time: 38.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1686140 = x;
        double r1686141 = y;
        double r1686142 = r1686140 + r1686141;
        double r1686143 = log(r1686142);
        double r1686144 = z;
        double r1686145 = log(r1686144);
        double r1686146 = r1686143 + r1686145;
        double r1686147 = t;
        double r1686148 = r1686146 - r1686147;
        double r1686149 = a;
        double r1686150 = 0.5;
        double r1686151 = r1686149 - r1686150;
        double r1686152 = log(r1686147);
        double r1686153 = r1686151 * r1686152;
        double r1686154 = r1686148 + r1686153;
        return r1686154;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1686155 = y;
        double r1686156 = x;
        double r1686157 = r1686155 + r1686156;
        double r1686158 = log(r1686157);
        double r1686159 = z;
        double r1686160 = cbrt(r1686159);
        double r1686161 = r1686160 * r1686160;
        double r1686162 = log(r1686161);
        double r1686163 = t;
        double r1686164 = log(r1686163);
        double r1686165 = a;
        double r1686166 = 0.5;
        double r1686167 = r1686165 - r1686166;
        double r1686168 = r1686164 * r1686167;
        double r1686169 = log(r1686160);
        double r1686170 = r1686169 - r1686163;
        double r1686171 = r1686168 + r1686170;
        double r1686172 = r1686162 + r1686171;
        double r1686173 = r1686158 + r1686172;
        return r1686173;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.2

    \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\]

  4. Applied associate-+l+0.2

    \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.2

    \[\leadsto \log \left(x + y\right) + \left(\left(\log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

  7. Applied log-prod0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

  8. Applied associate--l+0.3

    \[\leadsto \log \left(x + y\right) + \left(\color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\right)\]

  9. Applied associate-+l+0.3

    \[\leadsto \log \left(x + y\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\left(\log \left(\sqrt[3]{z}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)}\]

  10. Final simplification0.3

    \[\leadsto \log \left(y + x\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right)\right)\]

Reproduce

herbie shell --seed 2019142 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))