Average Error: 0.3 → 0.3
Time: 36.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\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(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r1455096 = x;
        double r1455097 = y;
        double r1455098 = r1455096 + r1455097;
        double r1455099 = log(r1455098);
        double r1455100 = z;
        double r1455101 = log(r1455100);
        double r1455102 = r1455099 + r1455101;
        double r1455103 = t;
        double r1455104 = r1455102 - r1455103;
        double r1455105 = a;
        double r1455106 = 0.5;
        double r1455107 = r1455105 - r1455106;
        double r1455108 = log(r1455103);
        double r1455109 = r1455107 * r1455108;
        double r1455110 = r1455104 + r1455109;
        return r1455110;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1455111 = y;
        double r1455112 = x;
        double r1455113 = r1455111 + r1455112;
        double r1455114 = cbrt(r1455113);
        double r1455115 = r1455114 * r1455114;
        double r1455116 = log(r1455115);
        double r1455117 = z;
        double r1455118 = log(r1455117);
        double r1455119 = log(r1455114);
        double r1455120 = r1455118 + r1455119;
        double r1455121 = r1455116 + r1455120;
        double r1455122 = t;
        double r1455123 = r1455121 - r1455122;
        double r1455124 = a;
        double r1455125 = 0.5;
        double r1455126 = r1455124 - r1455125;
        double r1455127 = log(r1455122);
        double r1455128 = r1455126 * r1455127;
        double r1455129 = r1455123 + r1455128;
        return r1455129;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019139 
(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))))