Average Error: 0.3 → 0.3
Time: 52.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log z + \left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(a - 0.5\right) \cdot \log t + \left(\log \left(\sqrt[3]{x + y}\right) - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log z + \left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(a - 0.5\right) \cdot \log t + \left(\log \left(\sqrt[3]{x + y}\right) - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2994814 = x;
        double r2994815 = y;
        double r2994816 = r2994814 + r2994815;
        double r2994817 = log(r2994816);
        double r2994818 = z;
        double r2994819 = log(r2994818);
        double r2994820 = r2994817 + r2994819;
        double r2994821 = t;
        double r2994822 = r2994820 - r2994821;
        double r2994823 = a;
        double r2994824 = 0.5;
        double r2994825 = r2994823 - r2994824;
        double r2994826 = log(r2994821);
        double r2994827 = r2994825 * r2994826;
        double r2994828 = r2994822 + r2994827;
        return r2994828;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2994829 = z;
        double r2994830 = log(r2994829);
        double r2994831 = x;
        double r2994832 = y;
        double r2994833 = r2994831 + r2994832;
        double r2994834 = cbrt(r2994833);
        double r2994835 = r2994834 * r2994834;
        double r2994836 = log(r2994835);
        double r2994837 = a;
        double r2994838 = 0.5;
        double r2994839 = r2994837 - r2994838;
        double r2994840 = t;
        double r2994841 = log(r2994840);
        double r2994842 = r2994839 * r2994841;
        double r2994843 = log(r2994834);
        double r2994844 = r2994843 - r2994840;
        double r2994845 = r2994842 + r2994844;
        double r2994846 = r2994836 + r2994845;
        double r2994847 = r2994830 + r2994846;
        return r2994847;
}

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. Simplified0.3

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

  4. Applied fma-udef0.3

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

  5. Applied associate-+r+0.3

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied associate--l+0.3

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

  10. Applied associate-+l+0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019112 +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))))