Average Error: 0.3 → 0.3
Time: 11.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left({\left(x + y\right)}^{\frac{1}{3}}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left({\left(x + y\right)}^{\frac{1}{3}}\right) + \log 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 r385755 = x;
        double r385756 = y;
        double r385757 = r385755 + r385756;
        double r385758 = log(r385757);
        double r385759 = z;
        double r385760 = log(r385759);
        double r385761 = r385758 + r385760;
        double r385762 = t;
        double r385763 = r385761 - r385762;
        double r385764 = a;
        double r385765 = 0.5;
        double r385766 = r385764 - r385765;
        double r385767 = log(r385762);
        double r385768 = r385766 * r385767;
        double r385769 = r385763 + r385768;
        return r385769;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r385770 = x;
        double r385771 = y;
        double r385772 = r385770 + r385771;
        double r385773 = cbrt(r385772);
        double r385774 = r385773 * r385773;
        double r385775 = log(r385774);
        double r385776 = 0.3333333333333333;
        double r385777 = pow(r385772, r385776);
        double r385778 = log(r385777);
        double r385779 = z;
        double r385780 = log(r385779);
        double r385781 = r385778 + r385780;
        double r385782 = r385775 + r385781;
        double r385783 = t;
        double r385784 = r385782 - r385783;
        double r385785 = a;
        double r385786 = 0.5;
        double r385787 = r385785 - r385786;
        double r385788 = log(r385783);
        double r385789 = r385787 * r385788;
        double r385790 = r385784 + r385789;
        return r385790;
}

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. Using strategy rm

  7. Applied pow1/30.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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