Average Error: 0.3 → 0.3
Time: 38.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r2146078 = x;
        double r2146079 = y;
        double r2146080 = r2146078 + r2146079;
        double r2146081 = log(r2146080);
        double r2146082 = z;
        double r2146083 = log(r2146082);
        double r2146084 = r2146081 + r2146083;
        double r2146085 = t;
        double r2146086 = r2146084 - r2146085;
        double r2146087 = a;
        double r2146088 = 0.5;
        double r2146089 = r2146087 - r2146088;
        double r2146090 = log(r2146085);
        double r2146091 = r2146089 * r2146090;
        double r2146092 = r2146086 + r2146091;
        return r2146092;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2146093 = t;
        double r2146094 = 0.3333333333333333;
        double r2146095 = pow(r2146093, r2146094);
        double r2146096 = log(r2146095);
        double r2146097 = a;
        double r2146098 = 0.5;
        double r2146099 = r2146097 - r2146098;
        double r2146100 = r2146096 * r2146099;
        double r2146101 = cbrt(r2146093);
        double r2146102 = log(r2146101);
        double r2146103 = r2146102 + r2146102;
        double r2146104 = r2146103 * r2146099;
        double r2146105 = r2146100 + r2146104;
        double r2146106 = y;
        double r2146107 = x;
        double r2146108 = r2146106 + r2146107;
        double r2146109 = cbrt(r2146108);
        double r2146110 = r2146109 * r2146109;
        double r2146111 = log(r2146110);
        double r2146112 = z;
        double r2146113 = log(r2146112);
        double r2146114 = log(r2146109);
        double r2146115 = r2146113 + r2146114;
        double r2146116 = r2146111 + r2146115;
        double r2146117 = r2146116 - r2146093;
        double r2146118 = r2146105 + r2146117;
        return r2146118;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  8. Applied pow1/30.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied log-prod0.3

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

  12. Applied associate-+l+0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))))