Average Error: 0.3 → 0.3
Time: 10.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r63658 = x;
        double r63659 = y;
        double r63660 = r63658 + r63659;
        double r63661 = log(r63660);
        double r63662 = z;
        double r63663 = log(r63662);
        double r63664 = r63661 + r63663;
        double r63665 = t;
        double r63666 = r63664 - r63665;
        double r63667 = a;
        double r63668 = 0.5;
        double r63669 = r63667 - r63668;
        double r63670 = log(r63665);
        double r63671 = r63669 * r63670;
        double r63672 = r63666 + r63671;
        return r63672;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r63673 = x;
        double r63674 = y;
        double r63675 = r63673 + r63674;
        double r63676 = cbrt(r63675);
        double r63677 = r63676 * r63676;
        double r63678 = log(r63677);
        double r63679 = log(r63676);
        double r63680 = z;
        double r63681 = log(r63680);
        double r63682 = t;
        double r63683 = r63681 - r63682;
        double r63684 = a;
        double r63685 = 0.5;
        double r63686 = r63684 - r63685;
        double r63687 = log(r63682);
        double r63688 = r63686 * r63687;
        double r63689 = r63683 + r63688;
        double r63690 = r63679 + r63689;
        double r63691 = r63678 + r63690;
        return r63691;
}

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

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

  4. Applied associate-+l+0.3

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))