Average Error: 0.3 → 0.3
Time: 46.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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(y + x\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 r3482081 = x;
        double r3482082 = y;
        double r3482083 = r3482081 + r3482082;
        double r3482084 = log(r3482083);
        double r3482085 = z;
        double r3482086 = log(r3482085);
        double r3482087 = r3482084 + r3482086;
        double r3482088 = t;
        double r3482089 = r3482087 - r3482088;
        double r3482090 = a;
        double r3482091 = 0.5;
        double r3482092 = r3482090 - r3482091;
        double r3482093 = log(r3482088);
        double r3482094 = r3482092 * r3482093;
        double r3482095 = r3482089 + r3482094;
        return r3482095;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3482096 = y;
        double r3482097 = x;
        double r3482098 = r3482096 + r3482097;
        double r3482099 = log(r3482098);
        double r3482100 = z;
        double r3482101 = cbrt(r3482100);
        double r3482102 = r3482101 * r3482101;
        double r3482103 = log(r3482102);
        double r3482104 = r3482099 + r3482103;
        double r3482105 = log(r3482101);
        double r3482106 = r3482104 + r3482105;
        double r3482107 = t;
        double r3482108 = r3482106 - r3482107;
        double r3482109 = a;
        double r3482110 = 0.5;
        double r3482111 = r3482109 - r3482110;
        double r3482112 = log(r3482107);
        double r3482113 = r3482111 * r3482112;
        double r3482114 = r3482108 + r3482113;
        return r3482114;
}

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

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

Reproduce

herbie shell --seed 2019119 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))