Average Error: 0.1 → 0.1
Time: 18.8s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11905788 = x;
        double r11905789 = y;
        double r11905790 = r11905788 * r11905789;
        double r11905791 = z;
        double r11905792 = t;
        double r11905793 = r11905791 * r11905792;
        double r11905794 = 16.0;
        double r11905795 = r11905793 / r11905794;
        double r11905796 = r11905790 + r11905795;
        double r11905797 = a;
        double r11905798 = b;
        double r11905799 = r11905797 * r11905798;
        double r11905800 = 4.0;
        double r11905801 = r11905799 / r11905800;
        double r11905802 = r11905796 - r11905801;
        double r11905803 = c;
        double r11905804 = r11905802 + r11905803;
        return r11905804;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11905805 = z;
        double r11905806 = t;
        double r11905807 = 16.0;
        double r11905808 = r11905806 / r11905807;
        double r11905809 = r11905805 * r11905808;
        double r11905810 = x;
        double r11905811 = y;
        double r11905812 = r11905810 * r11905811;
        double r11905813 = r11905809 + r11905812;
        double r11905814 = a;
        double r11905815 = b;
        double r11905816 = r11905814 * r11905815;
        double r11905817 = 4.0;
        double r11905818 = r11905816 / r11905817;
        double r11905819 = r11905813 - r11905818;
        double r11905820 = c;
        double r11905821 = r11905819 + r11905820;
        return r11905821;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{\color{blue}{1 \cdot 16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z}{1} \cdot \frac{t}{16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  5. Simplified0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{z} \cdot \frac{t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  6. Final simplification0.1

    \[\leadsto \left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))