Average Error: 0.3 → 0.3
Time: 13.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\]
\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 z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t, double a) {
        double r81998 = x;
        double r81999 = y;
        double r82000 = r81998 + r81999;
        double r82001 = log(r82000);
        double r82002 = z;
        double r82003 = log(r82002);
        double r82004 = r82001 + r82003;
        double r82005 = t;
        double r82006 = r82004 - r82005;
        double r82007 = a;
        double r82008 = 0.5;
        double r82009 = r82007 - r82008;
        double r82010 = log(r82005);
        double r82011 = r82009 * r82010;
        double r82012 = r82006 + r82011;
        return r82012;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r82013 = x;
        double r82014 = y;
        double r82015 = r82013 + r82014;
        double r82016 = log(r82015);
        double r82017 = z;
        double r82018 = log(r82017);
        double r82019 = r82016 + r82018;
        double r82020 = t;
        double r82021 = r82019 - r82020;
        double r82022 = sqrt(r82020);
        double r82023 = log(r82022);
        double r82024 = a;
        double r82025 = 0.5;
        double r82026 = r82024 - r82025;
        double r82027 = r82023 * r82026;
        double r82028 = r82021 + r82027;
        double r82029 = r82026 * r82023;
        double r82030 = r82028 + r82029;
        return r82030;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019362 
(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))))