Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(y \cdot i + \left(t + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)\right) + \left(\left(x \cdot \log 1 + z\right) + \left(\log y \cdot x\right) \cdot 1\right)\]
\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(y \cdot i + \left(t + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)\right) + \left(\left(x \cdot \log 1 + z\right) + \left(\log y \cdot x\right) \cdot 1\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80790 = x;
        double r80791 = y;
        double r80792 = log(r80791);
        double r80793 = r80790 * r80792;
        double r80794 = z;
        double r80795 = r80793 + r80794;
        double r80796 = t;
        double r80797 = r80795 + r80796;
        double r80798 = a;
        double r80799 = r80797 + r80798;
        double r80800 = b;
        double r80801 = 0.5;
        double r80802 = r80800 - r80801;
        double r80803 = c;
        double r80804 = log(r80803);
        double r80805 = r80802 * r80804;
        double r80806 = r80799 + r80805;
        double r80807 = i;
        double r80808 = r80791 * r80807;
        double r80809 = r80806 + r80808;
        return r80809;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80810 = y;
        double r80811 = i;
        double r80812 = r80810 * r80811;
        double r80813 = t;
        double r80814 = a;
        double r80815 = b;
        double r80816 = 0.5;
        double r80817 = r80815 - r80816;
        double r80818 = c;
        double r80819 = log(r80818);
        double r80820 = r80817 * r80819;
        double r80821 = r80814 + r80820;
        double r80822 = r80813 + r80821;
        double r80823 = r80812 + r80822;
        double r80824 = x;
        double r80825 = 1.0;
        double r80826 = log(r80825);
        double r80827 = r80824 * r80826;
        double r80828 = z;
        double r80829 = r80827 + r80828;
        double r80830 = log(r80810);
        double r80831 = r80830 * r80824;
        double r80832 = r80831 * r80825;
        double r80833 = r80829 + r80832;
        double r80834 = r80823 + r80833;
        return r80834;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied *-un-lft-identity0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

    \[\leadsto \left(y \cdot i + \left(t + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)\right) + \left(\left(x \cdot \log 1 + z\right) + \left(\log y \cdot x\right) \cdot 1\right)\]

Reproduce

herbie shell --seed 2019308 
(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)))