Average Error: 0.3 → 0.3
Time: 35.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r2721723 = x;
        double r2721724 = y;
        double r2721725 = r2721723 + r2721724;
        double r2721726 = log(r2721725);
        double r2721727 = z;
        double r2721728 = log(r2721727);
        double r2721729 = r2721726 + r2721728;
        double r2721730 = t;
        double r2721731 = r2721729 - r2721730;
        double r2721732 = a;
        double r2721733 = 0.5;
        double r2721734 = r2721732 - r2721733;
        double r2721735 = log(r2721730);
        double r2721736 = r2721734 * r2721735;
        double r2721737 = r2721731 + r2721736;
        return r2721737;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2721738 = a;
        double r2721739 = 0.5;
        double r2721740 = r2721738 - r2721739;
        double r2721741 = t;
        double r2721742 = 0.3333333333333333;
        double r2721743 = pow(r2721741, r2721742);
        double r2721744 = log(r2721743);
        double r2721745 = r2721740 * r2721744;
        double r2721746 = cbrt(r2721741);
        double r2721747 = log(r2721746);
        double r2721748 = r2721740 * r2721747;
        double r2721749 = r2721748 + r2721748;
        double r2721750 = r2721745 + r2721749;
        double r2721751 = y;
        double r2721752 = x;
        double r2721753 = r2721751 + r2721752;
        double r2721754 = log(r2721753);
        double r2721755 = z;
        double r2721756 = log(r2721755);
        double r2721757 = r2721754 + r2721756;
        double r2721758 = r2721757 - r2721741;
        double r2721759 = r2721750 + r2721758;
        return r2721759;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  8. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({t}^{\frac{1}{3}}\right)}\right)\]

  9. Final simplification0.3

    \[\leadsto \left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

Reproduce

herbie shell --seed 2019163 +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))))