Average Error: 0.3 → 0.3
Time: 13.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r67048 = x;
        double r67049 = y;
        double r67050 = r67048 + r67049;
        double r67051 = log(r67050);
        double r67052 = z;
        double r67053 = log(r67052);
        double r67054 = r67051 + r67053;
        double r67055 = t;
        double r67056 = r67054 - r67055;
        double r67057 = a;
        double r67058 = 0.5;
        double r67059 = r67057 - r67058;
        double r67060 = log(r67055);
        double r67061 = r67059 * r67060;
        double r67062 = r67056 + r67061;
        return r67062;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r67063 = x;
        double r67064 = y;
        double r67065 = r67063 + r67064;
        double r67066 = log(r67065);
        double r67067 = z;
        double r67068 = log(r67067);
        double r67069 = t;
        double r67070 = r67068 - r67069;
        double r67071 = a;
        double r67072 = 0.5;
        double r67073 = r67071 - r67072;
        double r67074 = sqrt(r67069);
        double r67075 = log(r67074);
        double r67076 = r67073 * r67075;
        double r67077 = r67076 + r67076;
        double r67078 = r67070 + r67077;
        double r67079 = r67066 + r67078;
        return r67079;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  6. Applied add-sqr-sqrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied distribute-lft-in0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020034 
(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))))