Average Error: 0.0 → 0.7
Time: 16.8s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(z \cdot t + x \cdot y\right) + \left(\sqrt[3]{c \cdot i + a \cdot b} \cdot \sqrt[3]{c \cdot i + a \cdot b}\right) \cdot \sqrt[3]{c \cdot i + a \cdot b}\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\left(z \cdot t + x \cdot y\right) + \left(\sqrt[3]{c \cdot i + a \cdot b} \cdot \sqrt[3]{c \cdot i + a \cdot b}\right) \cdot \sqrt[3]{c \cdot i + a \cdot b}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6757841 = x;
        double r6757842 = y;
        double r6757843 = r6757841 * r6757842;
        double r6757844 = z;
        double r6757845 = t;
        double r6757846 = r6757844 * r6757845;
        double r6757847 = r6757843 + r6757846;
        double r6757848 = a;
        double r6757849 = b;
        double r6757850 = r6757848 * r6757849;
        double r6757851 = r6757847 + r6757850;
        double r6757852 = c;
        double r6757853 = i;
        double r6757854 = r6757852 * r6757853;
        double r6757855 = r6757851 + r6757854;
        return r6757855;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6757856 = z;
        double r6757857 = t;
        double r6757858 = r6757856 * r6757857;
        double r6757859 = x;
        double r6757860 = y;
        double r6757861 = r6757859 * r6757860;
        double r6757862 = r6757858 + r6757861;
        double r6757863 = c;
        double r6757864 = i;
        double r6757865 = r6757863 * r6757864;
        double r6757866 = a;
        double r6757867 = b;
        double r6757868 = r6757866 * r6757867;
        double r6757869 = r6757865 + r6757868;
        double r6757870 = cbrt(r6757869);
        double r6757871 = r6757870 * r6757870;
        double r6757872 = r6757871 * r6757870;
        double r6757873 = r6757862 + r6757872;
        return r6757873;
}

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 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

    \[\leadsto \color{blue}{\left(x \cdot y + z \cdot t\right) + \left(a \cdot b + c \cdot i\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))