Average Error: 0.3 → 0.3
Time: 53.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r3174135 = x;
        double r3174136 = y;
        double r3174137 = r3174135 + r3174136;
        double r3174138 = log(r3174137);
        double r3174139 = z;
        double r3174140 = log(r3174139);
        double r3174141 = r3174138 + r3174140;
        double r3174142 = t;
        double r3174143 = r3174141 - r3174142;
        double r3174144 = a;
        double r3174145 = 0.5;
        double r3174146 = r3174144 - r3174145;
        double r3174147 = log(r3174142);
        double r3174148 = r3174146 * r3174147;
        double r3174149 = r3174143 + r3174148;
        return r3174149;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3174150 = y;
        double r3174151 = x;
        double r3174152 = r3174150 + r3174151;
        double r3174153 = cbrt(r3174152);
        double r3174154 = r3174153 * r3174153;
        double r3174155 = log(r3174154);
        double r3174156 = z;
        double r3174157 = log(r3174156);
        double r3174158 = log(r3174153);
        double r3174159 = r3174157 + r3174158;
        double r3174160 = r3174155 + r3174159;
        double r3174161 = t;
        double r3174162 = r3174160 - r3174161;
        double r3174163 = a;
        double r3174164 = 0.5;
        double r3174165 = r3174163 - r3174164;
        double r3174166 = log(r3174161);
        double r3174167 = r3174165 * r3174166;
        double r3174168 = r3174162 + r3174167;
        return r3174168;
}

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 0.3

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

  3. Applied add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(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))))