Average Error: 0.3 → 0.3
Time: 11.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{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 r63023 = x;
        double r63024 = y;
        double r63025 = r63023 + r63024;
        double r63026 = log(r63025);
        double r63027 = z;
        double r63028 = log(r63027);
        double r63029 = r63026 + r63028;
        double r63030 = t;
        double r63031 = r63029 - r63030;
        double r63032 = a;
        double r63033 = 0.5;
        double r63034 = r63032 - r63033;
        double r63035 = log(r63030);
        double r63036 = r63034 * r63035;
        double r63037 = r63031 + r63036;
        return r63037;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r63038 = x;
        double r63039 = y;
        double r63040 = r63038 + r63039;
        double r63041 = log(r63040);
        double r63042 = z;
        double r63043 = cbrt(r63042);
        double r63044 = r63043 * r63043;
        double r63045 = log(r63044);
        double r63046 = r63041 + r63045;
        double r63047 = log(r63043);
        double r63048 = r63046 + r63047;
        double r63049 = t;
        double r63050 = r63048 - r63049;
        double r63051 = a;
        double r63052 = 0.5;
        double r63053 = r63051 - r63052;
        double r63054 = log(r63049);
        double r63055 = r63053 * r63054;
        double r63056 = r63050 + r63055;
        return r63056;
}

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

    \[\leadsto \left(\left(\log \left(x + y\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Applied associate-+r+0.3

    \[\leadsto \left(\color{blue}{\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  6. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2020021 
(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))))