Average Error: 0.3 → 0.3
Time: 50.4s
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 r3132598 = x;
        double r3132599 = y;
        double r3132600 = r3132598 + r3132599;
        double r3132601 = log(r3132600);
        double r3132602 = z;
        double r3132603 = log(r3132602);
        double r3132604 = r3132601 + r3132603;
        double r3132605 = t;
        double r3132606 = r3132604 - r3132605;
        double r3132607 = a;
        double r3132608 = 0.5;
        double r3132609 = r3132607 - r3132608;
        double r3132610 = log(r3132605);
        double r3132611 = r3132609 * r3132610;
        double r3132612 = r3132606 + r3132611;
        return r3132612;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3132613 = y;
        double r3132614 = x;
        double r3132615 = r3132613 + r3132614;
        double r3132616 = log(r3132615);
        double r3132617 = z;
        double r3132618 = cbrt(r3132617);
        double r3132619 = r3132618 * r3132618;
        double r3132620 = log(r3132619);
        double r3132621 = r3132616 + r3132620;
        double r3132622 = log(r3132618);
        double r3132623 = r3132621 + r3132622;
        double r3132624 = t;
        double r3132625 = r3132623 - r3132624;
        double r3132626 = a;
        double r3132627 = 0.5;
        double r3132628 = r3132626 - r3132627;
        double r3132629 = log(r3132624);
        double r3132630 = r3132628 * r3132629;
        double r3132631 = r3132625 + r3132630;
        return r3132631;
}

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 +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))))