Average Error: 0.1 → 0.1
Time: 1.3m
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(x \cdot \log \left(\sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\left(x \cdot \log \left(\sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4111687 = x;
        double r4111688 = y;
        double r4111689 = log(r4111688);
        double r4111690 = r4111687 * r4111689;
        double r4111691 = z;
        double r4111692 = r4111690 + r4111691;
        double r4111693 = t;
        double r4111694 = r4111692 + r4111693;
        double r4111695 = a;
        double r4111696 = r4111694 + r4111695;
        double r4111697 = b;
        double r4111698 = 0.5;
        double r4111699 = r4111697 - r4111698;
        double r4111700 = c;
        double r4111701 = log(r4111700);
        double r4111702 = r4111699 * r4111701;
        double r4111703 = r4111696 + r4111702;
        double r4111704 = i;
        double r4111705 = r4111688 * r4111704;
        double r4111706 = r4111703 + r4111705;
        return r4111706;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4111707 = z;
        double r4111708 = x;
        double r4111709 = y;
        double r4111710 = cbrt(r4111709);
        double r4111711 = log(r4111710);
        double r4111712 = r4111708 * r4111711;
        double r4111713 = cbrt(r4111710);
        double r4111714 = r4111713 * r4111713;
        double r4111715 = r4111713 * r4111714;
        double r4111716 = log(r4111715);
        double r4111717 = r4111708 * r4111716;
        double r4111718 = r4111712 + r4111717;
        double r4111719 = r4111718 + r4111712;
        double r4111720 = r4111707 + r4111719;
        double r4111721 = t;
        double r4111722 = r4111720 + r4111721;
        double r4111723 = a;
        double r4111724 = r4111722 + r4111723;
        double r4111725 = c;
        double r4111726 = log(r4111725);
        double r4111727 = b;
        double r4111728 = 0.5;
        double r4111729 = r4111727 - r4111728;
        double r4111730 = r4111726 * r4111729;
        double r4111731 = r4111724 + r4111730;
        double r4111732 = i;
        double r4111733 = r4111709 * r4111732;
        double r4111734 = r4111731 + r4111733;
        return r4111734;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(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)))