Average Error: 0.3 → 0.3
Time: 34.5s
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 r17439808 = x;
        double r17439809 = y;
        double r17439810 = r17439808 + r17439809;
        double r17439811 = log(r17439810);
        double r17439812 = z;
        double r17439813 = log(r17439812);
        double r17439814 = r17439811 + r17439813;
        double r17439815 = t;
        double r17439816 = r17439814 - r17439815;
        double r17439817 = a;
        double r17439818 = 0.5;
        double r17439819 = r17439817 - r17439818;
        double r17439820 = log(r17439815);
        double r17439821 = r17439819 * r17439820;
        double r17439822 = r17439816 + r17439821;
        return r17439822;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r17439823 = y;
        double r17439824 = x;
        double r17439825 = r17439823 + r17439824;
        double r17439826 = cbrt(r17439825);
        double r17439827 = r17439826 * r17439826;
        double r17439828 = log(r17439827);
        double r17439829 = z;
        double r17439830 = log(r17439829);
        double r17439831 = log(r17439826);
        double r17439832 = r17439830 + r17439831;
        double r17439833 = r17439828 + r17439832;
        double r17439834 = t;
        double r17439835 = r17439833 - r17439834;
        double r17439836 = a;
        double r17439837 = 0.5;
        double r17439838 = r17439836 - r17439837;
        double r17439839 = log(r17439834);
        double r17439840 = r17439838 * r17439839;
        double r17439841 = r17439835 + r17439840;
        return r17439841;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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 2019170 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))