Average Error: 0.3 → 0.3
Time: 50.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
double f(double x, double y, double z, double t, double a) {
        double r2756676 = x;
        double r2756677 = y;
        double r2756678 = r2756676 + r2756677;
        double r2756679 = log(r2756678);
        double r2756680 = z;
        double r2756681 = log(r2756680);
        double r2756682 = r2756679 + r2756681;
        double r2756683 = t;
        double r2756684 = r2756682 - r2756683;
        double r2756685 = a;
        double r2756686 = 0.5;
        double r2756687 = r2756685 - r2756686;
        double r2756688 = log(r2756683);
        double r2756689 = r2756687 * r2756688;
        double r2756690 = r2756684 + r2756689;
        return r2756690;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2756691 = y;
        double r2756692 = x;
        double r2756693 = r2756691 + r2756692;
        double r2756694 = cbrt(r2756693);
        double r2756695 = r2756694 * r2756694;
        double r2756696 = log(r2756695);
        double r2756697 = z;
        double r2756698 = log(r2756697);
        double r2756699 = log(r2756694);
        double r2756700 = r2756698 + r2756699;
        double r2756701 = r2756696 + r2756700;
        double r2756702 = t;
        double r2756703 = r2756701 - r2756702;
        double r2756704 = a;
        double r2756705 = 0.5;
        double r2756706 = r2756704 - r2756705;
        double r2756707 = log(r2756702);
        double r2756708 = r2756706 * r2756707;
        double r2756709 = r2756703 + r2756708;
        return r2756709;
}


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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019101 +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))))