Average Error: 0.3 → 0.3
Time: 32.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) - \left(\left(t - \log z\right) - \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \left(\frac{1}{3} \cdot \log t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) - \left(\left(t - \log z\right) - \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \left(\frac{1}{3} \cdot \log t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r72155 = x;
        double r72156 = y;
        double r72157 = r72155 + r72156;
        double r72158 = log(r72157);
        double r72159 = z;
        double r72160 = log(r72159);
        double r72161 = r72158 + r72160;
        double r72162 = t;
        double r72163 = r72161 - r72162;
        double r72164 = a;
        double r72165 = 0.5;
        double r72166 = r72164 - r72165;
        double r72167 = log(r72162);
        double r72168 = r72166 * r72167;
        double r72169 = r72163 + r72168;
        return r72169;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r72170 = x;
        double r72171 = y;
        double r72172 = r72170 + r72171;
        double r72173 = log(r72172);
        double r72174 = t;
        double r72175 = z;
        double r72176 = log(r72175);
        double r72177 = r72174 - r72176;
        double r72178 = a;
        double r72179 = 0.5;
        double r72180 = r72178 - r72179;
        double r72181 = 2.0;
        double r72182 = cbrt(r72174);
        double r72183 = log(r72182);
        double r72184 = r72181 * r72183;
        double r72185 = r72180 * r72184;
        double r72186 = 0.3333333333333333;
        double r72187 = log(r72174);
        double r72188 = r72186 * r72187;
        double r72189 = r72180 * r72188;
        double r72190 = r72185 + r72189;
        double r72191 = r72177 - r72190;
        double r72192 = r72173 - r72191;
        return r72192;
}

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. Simplified0.3

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

  4. Applied add-cube-cbrt0.3

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

  5. Applied log-prod0.3

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

  6. Applied distribute-lft-in0.3

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

  7. Simplified0.3

    \[\leadsto \log \left(y + x\right) - \left(\left(t - \log z\right) - \left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]

  8. Taylor expanded around inf 0.3

    \[\leadsto \log \left(y + x\right) - \left(\left(t - \log z\right) - \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \color{blue}{\left(a \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) - 0.5 \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\right)}\right)\right)\]

  9. Simplified0.3

    \[\leadsto \log \left(y + x\right) - \left(\left(t - \log z\right) - \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\frac{-1}{3} \cdot \log t\right)}\right)\right)\]

  10. Final simplification0.3

    \[\leadsto \log \left(x + y\right) - \left(\left(t - \log z\right) - \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \left(\frac{1}{3} \cdot \log t\right)\right)\right)\]

Reproduce

herbie shell --seed 2019194 
(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))))