Average Error: 0.3 → 0.3
Time: 11.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\log z - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\log z - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r75065 = x;
        double r75066 = y;
        double r75067 = r75065 + r75066;
        double r75068 = log(r75067);
        double r75069 = z;
        double r75070 = log(r75069);
        double r75071 = r75068 + r75070;
        double r75072 = t;
        double r75073 = r75071 - r75072;
        double r75074 = a;
        double r75075 = 0.5;
        double r75076 = r75074 - r75075;
        double r75077 = log(r75072);
        double r75078 = r75076 * r75077;
        double r75079 = r75073 + r75078;
        return r75079;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r75080 = x;
        double r75081 = y;
        double r75082 = r75080 + r75081;
        double r75083 = sqrt(r75082);
        double r75084 = log(r75083);
        double r75085 = z;
        double r75086 = log(r75085);
        double r75087 = t;
        double r75088 = r75086 - r75087;
        double r75089 = r75084 + r75088;
        double r75090 = r75084 + r75089;
        double r75091 = a;
        double r75092 = 0.5;
        double r75093 = r75091 - r75092;
        double r75094 = log(r75087);
        double r75095 = r75093 * r75094;
        double r75096 = r75090 + r75095;
        return r75096;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))))