Average Error: 0.1 → 0.1
Time: 17.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + 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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r98711 = x;
        double r98712 = y;
        double r98713 = log(r98712);
        double r98714 = r98711 * r98713;
        double r98715 = z;
        double r98716 = r98714 + r98715;
        double r98717 = t;
        double r98718 = r98716 + r98717;
        double r98719 = a;
        double r98720 = r98718 + r98719;
        double r98721 = b;
        double r98722 = 0.5;
        double r98723 = r98721 - r98722;
        double r98724 = c;
        double r98725 = log(r98724);
        double r98726 = r98723 * r98725;
        double r98727 = r98720 + r98726;
        double r98728 = i;
        double r98729 = r98712 * r98728;
        double r98730 = r98727 + r98729;
        return r98730;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r98731 = 2.0;
        double r98732 = y;
        double r98733 = cbrt(r98732);
        double r98734 = log(r98733);
        double r98735 = r98731 * r98734;
        double r98736 = x;
        double r98737 = r98735 * r98736;
        double r98738 = r98736 * r98734;
        double r98739 = r98737 + r98738;
        double r98740 = z;
        double r98741 = r98739 + r98740;
        double r98742 = t;
        double r98743 = r98741 + r98742;
        double r98744 = a;
        double r98745 = r98743 + r98744;
        double r98746 = b;
        double r98747 = 0.5;
        double r98748 = r98746 - r98747;
        double r98749 = c;
        double r98750 = log(r98749);
        double r98751 = r98748 * r98750;
        double r98752 = r98745 + r98751;
        double r98753 = i;
        double r98754 = r98732 * r98753;
        double r98755 = r98752 + r98754;
        return r98755;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))