Average Error: 0.3 → 0.3
Time: 37.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r2061077 = x;
        double r2061078 = y;
        double r2061079 = r2061077 + r2061078;
        double r2061080 = log(r2061079);
        double r2061081 = z;
        double r2061082 = log(r2061081);
        double r2061083 = r2061080 + r2061082;
        double r2061084 = t;
        double r2061085 = r2061083 - r2061084;
        double r2061086 = a;
        double r2061087 = 0.5;
        double r2061088 = r2061086 - r2061087;
        double r2061089 = log(r2061084);
        double r2061090 = r2061088 * r2061089;
        double r2061091 = r2061085 + r2061090;
        return r2061091;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2061092 = y;
        double r2061093 = x;
        double r2061094 = r2061092 + r2061093;
        double r2061095 = 0.6666666666666666;
        double r2061096 = pow(r2061094, r2061095);
        double r2061097 = log(r2061096);
        double r2061098 = z;
        double r2061099 = log(r2061098);
        double r2061100 = 0.3333333333333333;
        double r2061101 = pow(r2061094, r2061100);
        double r2061102 = log(r2061101);
        double r2061103 = r2061099 + r2061102;
        double r2061104 = r2061097 + r2061103;
        double r2061105 = t;
        double r2061106 = r2061104 - r2061105;
        double r2061107 = log(r2061105);
        double r2061108 = a;
        double r2061109 = 0.5;
        double r2061110 = r2061108 - r2061109;
        double r2061111 = r2061107 * r2061110;
        double r2061112 = r2061106 + r2061111;
        return r2061112;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(\sqrt[3]{x + y} \cdot \color{blue}{{\left(x + y\right)}^{\frac{1}{3}}}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  8. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(\color{blue}{{\left(x + y\right)}^{\frac{1}{3}}} \cdot {\left(x + y\right)}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  9. Applied pow-prod-up0.3

    \[\leadsto \left(\left(\log \color{blue}{\left({\left(x + y\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right)} + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  10. Simplified0.3

    \[\leadsto \left(\left(\log \left({\left(x + y\right)}^{\color{blue}{\frac{2}{3}}}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  11. Using strategy rm

  12. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left({\left(x + y\right)}^{\frac{2}{3}}\right) + \left(\log \color{blue}{\left({\left(x + y\right)}^{\frac{1}{3}}\right)} + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  13. Final simplification0.3

    \[\leadsto \left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019130 
(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))))