Average Error: 0.3 → 0.3
Time: 40.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\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 r2317212 = x;
        double r2317213 = y;
        double r2317214 = r2317212 + r2317213;
        double r2317215 = log(r2317214);
        double r2317216 = z;
        double r2317217 = log(r2317216);
        double r2317218 = r2317215 + r2317217;
        double r2317219 = t;
        double r2317220 = r2317218 - r2317219;
        double r2317221 = a;
        double r2317222 = 0.5;
        double r2317223 = r2317221 - r2317222;
        double r2317224 = log(r2317219);
        double r2317225 = r2317223 * r2317224;
        double r2317226 = r2317220 + r2317225;
        return r2317226;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2317227 = y;
        double r2317228 = x;
        double r2317229 = r2317227 + r2317228;
        double r2317230 = log(r2317229);
        double r2317231 = z;
        double r2317232 = cbrt(r2317231);
        double r2317233 = r2317232 * r2317232;
        double r2317234 = log(r2317233);
        double r2317235 = r2317230 + r2317234;
        double r2317236 = log(r2317232);
        double r2317237 = r2317235 + r2317236;
        double r2317238 = t;
        double r2317239 = r2317237 - r2317238;
        double r2317240 = a;
        double r2317241 = 0.5;
        double r2317242 = r2317240 - r2317241;
        double r2317243 = log(r2317238);
        double r2317244 = r2317242 * r2317243;
        double r2317245 = r2317239 + r2317244;
        return r2317245;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019124 
(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))))