Average Error: 0.1 → 0.2
Time: 29.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left({\left({\left(\frac{1}{y}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left({\left({\left(\frac{1}{y}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82713 = x;
        double r82714 = y;
        double r82715 = log(r82714);
        double r82716 = r82713 * r82715;
        double r82717 = z;
        double r82718 = r82716 + r82717;
        double r82719 = t;
        double r82720 = r82718 + r82719;
        double r82721 = a;
        double r82722 = r82720 + r82721;
        double r82723 = b;
        double r82724 = 0.5;
        double r82725 = r82723 - r82724;
        double r82726 = c;
        double r82727 = log(r82726);
        double r82728 = r82725 * r82727;
        double r82729 = r82722 + r82728;
        double r82730 = i;
        double r82731 = r82714 * r82730;
        double r82732 = r82729 + r82731;
        return r82732;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82733 = y;
        double r82734 = cbrt(r82733);
        double r82735 = r82734 * r82734;
        double r82736 = log(r82735);
        double r82737 = x;
        double r82738 = r82736 * r82737;
        double r82739 = 1.0;
        double r82740 = r82739 / r82733;
        double r82741 = -0.3333333333333333;
        double r82742 = cbrt(r82741);
        double r82743 = r82742 * r82742;
        double r82744 = pow(r82740, r82743);
        double r82745 = pow(r82744, r82742);
        double r82746 = log(r82745);
        double r82747 = r82737 * r82746;
        double r82748 = z;
        double r82749 = r82747 + r82748;
        double r82750 = r82738 + r82749;
        double r82751 = t;
        double r82752 = r82750 + r82751;
        double r82753 = a;
        double r82754 = r82752 + r82753;
        double r82755 = b;
        double r82756 = 0.5;
        double r82757 = r82755 - r82756;
        double r82758 = c;
        double r82759 = log(r82758);
        double r82760 = r82757 * r82759;
        double r82761 = r82754 + r82760;
        double r82762 = i;
        double r82763 = r82733 * r82762;
        double r82764 = r82761 + r82763;
        return r82764;
}

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. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  8. Taylor expanded around inf 0.1

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

  10. Applied add-cube-cbrt0.2

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

  11. Applied pow-unpow0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019208 
(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)))