Average Error: 0.3 → 0.3
Time: 40.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(y + x\right) + \log z\right) - \left(t - \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(y + x\right) + \log z\right) - \left(t - \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2618197 = x;
        double r2618198 = y;
        double r2618199 = r2618197 + r2618198;
        double r2618200 = log(r2618199);
        double r2618201 = z;
        double r2618202 = log(r2618201);
        double r2618203 = r2618200 + r2618202;
        double r2618204 = t;
        double r2618205 = r2618203 - r2618204;
        double r2618206 = a;
        double r2618207 = 0.5;
        double r2618208 = r2618206 - r2618207;
        double r2618209 = log(r2618204);
        double r2618210 = r2618208 * r2618209;
        double r2618211 = r2618205 + r2618210;
        return r2618211;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2618212 = y;
        double r2618213 = x;
        double r2618214 = r2618212 + r2618213;
        double r2618215 = log(r2618214);
        double r2618216 = z;
        double r2618217 = log(r2618216);
        double r2618218 = r2618215 + r2618217;
        double r2618219 = t;
        double r2618220 = cbrt(r2618219);
        double r2618221 = log(r2618220);
        double r2618222 = a;
        double r2618223 = 0.5;
        double r2618224 = r2618222 - r2618223;
        double r2618225 = r2618221 * r2618224;
        double r2618226 = r2618225 + r2618225;
        double r2618227 = r2618225 + r2618226;
        double r2618228 = r2618219 - r2618227;
        double r2618229 = r2618218 - r2618228;
        return r2618229;
}

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 associate-+l-0.3

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied distribute-lft-in0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019135 +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))))