Average Error: 0.3 → 0.3
Time: 39.7s
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 r2276674 = x;
        double r2276675 = y;
        double r2276676 = r2276674 + r2276675;
        double r2276677 = log(r2276676);
        double r2276678 = z;
        double r2276679 = log(r2276678);
        double r2276680 = r2276677 + r2276679;
        double r2276681 = t;
        double r2276682 = r2276680 - r2276681;
        double r2276683 = a;
        double r2276684 = 0.5;
        double r2276685 = r2276683 - r2276684;
        double r2276686 = log(r2276681);
        double r2276687 = r2276685 * r2276686;
        double r2276688 = r2276682 + r2276687;
        return r2276688;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2276689 = a;
        double r2276690 = 0.5;
        double r2276691 = r2276689 - r2276690;
        double r2276692 = t;
        double r2276693 = 0.3333333333333333;
        double r2276694 = pow(r2276692, r2276693);
        double r2276695 = log(r2276694);
        double r2276696 = r2276691 * r2276695;
        double r2276697 = cbrt(r2276692);
        double r2276698 = log(r2276697);
        double r2276699 = r2276691 * r2276698;
        double r2276700 = r2276699 + r2276699;
        double r2276701 = r2276696 + r2276700;
        double r2276702 = y;
        double r2276703 = x;
        double r2276704 = r2276702 + r2276703;
        double r2276705 = log(r2276704);
        double r2276706 = z;
        double r2276707 = log(r2276706);
        double r2276708 = r2276705 + r2276707;
        double r2276709 = r2276708 - r2276692;
        double r2276710 = r2276701 + r2276709;
        return r2276710;
}

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))))