Average Error: 0.1 → 0.1
Time: 51.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69757 = x;
        double r69758 = y;
        double r69759 = log(r69758);
        double r69760 = r69757 * r69759;
        double r69761 = z;
        double r69762 = r69760 + r69761;
        double r69763 = t;
        double r69764 = r69762 + r69763;
        double r69765 = a;
        double r69766 = r69764 + r69765;
        double r69767 = b;
        double r69768 = 0.5;
        double r69769 = r69767 - r69768;
        double r69770 = c;
        double r69771 = log(r69770);
        double r69772 = r69769 * r69771;
        double r69773 = r69766 + r69772;
        double r69774 = i;
        double r69775 = r69758 * r69774;
        double r69776 = r69773 + r69775;
        return r69776;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69777 = x;
        double r69778 = y;
        double r69779 = log(r69778);
        double r69780 = r69777 * r69779;
        double r69781 = z;
        double r69782 = r69780 + r69781;
        double r69783 = t;
        double r69784 = r69782 + r69783;
        double r69785 = a;
        double r69786 = r69784 + r69785;
        double r69787 = 2.0;
        double r69788 = c;
        double r69789 = cbrt(r69788);
        double r69790 = log(r69789);
        double r69791 = r69787 * r69790;
        double r69792 = b;
        double r69793 = 0.5;
        double r69794 = r69792 - r69793;
        double r69795 = r69791 * r69794;
        double r69796 = r69786 + r69795;
        double r69797 = 0.3333333333333333;
        double r69798 = pow(r69788, r69797);
        double r69799 = log(r69798);
        double r69800 = r69794 * r69799;
        double r69801 = r69796 + r69800;
        double r69802 = i;
        double r69803 = r69778 * r69802;
        double r69804 = r69801 + r69803;
        return r69804;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))