Average Error: 0.1 → 0.1
Time: 44.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right)\right)\right)\right) + i \cdot y\]
\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(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right)\right)\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4229743 = x;
        double r4229744 = y;
        double r4229745 = log(r4229744);
        double r4229746 = r4229743 * r4229745;
        double r4229747 = z;
        double r4229748 = r4229746 + r4229747;
        double r4229749 = t;
        double r4229750 = r4229748 + r4229749;
        double r4229751 = a;
        double r4229752 = r4229750 + r4229751;
        double r4229753 = b;
        double r4229754 = 0.5;
        double r4229755 = r4229753 - r4229754;
        double r4229756 = c;
        double r4229757 = log(r4229756);
        double r4229758 = r4229755 * r4229757;
        double r4229759 = r4229752 + r4229758;
        double r4229760 = i;
        double r4229761 = r4229744 * r4229760;
        double r4229762 = r4229759 + r4229761;
        return r4229762;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4229763 = b;
        double r4229764 = 0.5;
        double r4229765 = r4229763 - r4229764;
        double r4229766 = c;
        double r4229767 = log(r4229766);
        double r4229768 = r4229765 * r4229767;
        double r4229769 = a;
        double r4229770 = t;
        double r4229771 = y;
        double r4229772 = cbrt(r4229771);
        double r4229773 = log(r4229772);
        double r4229774 = r4229773 + r4229773;
        double r4229775 = x;
        double r4229776 = r4229774 * r4229775;
        double r4229777 = r4229773 * r4229775;
        double r4229778 = r4229776 + r4229777;
        double r4229779 = z;
        double r4229780 = r4229778 + r4229779;
        double r4229781 = r4229770 + r4229780;
        double r4229782 = r4229769 + r4229781;
        double r4229783 = r4229768 + r4229782;
        double r4229784 = i;
        double r4229785 = r4229784 * r4229771;
        double r4229786 = r4229783 + r4229785;
        return r4229786;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))