Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - a \cdot \frac{b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - a \cdot \frac{b}{4}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r195851 = x;
        double r195852 = y;
        double r195853 = r195851 * r195852;
        double r195854 = z;
        double r195855 = t;
        double r195856 = r195854 * r195855;
        double r195857 = 16.0;
        double r195858 = r195856 / r195857;
        double r195859 = r195853 + r195858;
        double r195860 = a;
        double r195861 = b;
        double r195862 = r195860 * r195861;
        double r195863 = 4.0;
        double r195864 = r195862 / r195863;
        double r195865 = r195859 - r195864;
        double r195866 = c;
        double r195867 = r195865 + r195866;
        return r195867;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r195868 = x;
        double r195869 = y;
        double r195870 = r195868 * r195869;
        double r195871 = z;
        double r195872 = t;
        double r195873 = r195871 * r195872;
        double r195874 = 16.0;
        double r195875 = r195873 / r195874;
        double r195876 = r195870 + r195875;
        double r195877 = a;
        double r195878 = b;
        double r195879 = 4.0;
        double r195880 = r195878 / r195879;
        double r195881 = r195877 * r195880;
        double r195882 = r195876 - r195881;
        double r195883 = c;
        double r195884 = r195882 + r195883;
        return r195884;
}

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

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
  2. Using strategy rm

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

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{\color{blue}{1 \cdot 4}}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \color{blue}{\frac{a}{1} \cdot \frac{b}{4}}\right) + c\]

  5. Simplified0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \color{blue}{a} \cdot \frac{b}{4}\right) + c\]

  6. Final simplification0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - a \cdot \frac{b}{4}\right) + c\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))