Average Error: 0.3 → 0.3
Time: 17.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\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 r55689 = x;
        double r55690 = y;
        double r55691 = r55689 + r55690;
        double r55692 = log(r55691);
        double r55693 = z;
        double r55694 = log(r55693);
        double r55695 = r55692 + r55694;
        double r55696 = t;
        double r55697 = r55695 - r55696;
        double r55698 = a;
        double r55699 = 0.5;
        double r55700 = r55698 - r55699;
        double r55701 = log(r55696);
        double r55702 = r55700 * r55701;
        double r55703 = r55697 + r55702;
        return r55703;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55704 = x;
        double r55705 = y;
        double r55706 = r55704 + r55705;
        double r55707 = log(r55706);
        double r55708 = z;
        double r55709 = sqrt(r55708);
        double r55710 = log(r55709);
        double r55711 = r55707 + r55710;
        double r55712 = r55711 + r55710;
        double r55713 = t;
        double r55714 = r55712 - r55713;
        double r55715 = a;
        double r55716 = 0.5;
        double r55717 = r55715 - r55716;
        double r55718 = log(r55713);
        double r55719 = r55717 * r55718;
        double r55720 = r55714 + r55719;
        return r55720;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))