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 r12698774 = x;
        double r12698775 = y;
        double r12698776 = r12698774 * r12698775;
        double r12698777 = z;
        double r12698778 = t;
        double r12698779 = r12698777 * r12698778;
        double r12698780 = 16.0;
        double r12698781 = r12698779 / r12698780;
        double r12698782 = r12698776 + r12698781;
        double r12698783 = a;
        double r12698784 = b;
        double r12698785 = r12698783 * r12698784;
        double r12698786 = 4.0;
        double r12698787 = r12698785 / r12698786;
        double r12698788 = r12698782 - r12698787;
        double r12698789 = c;
        double r12698790 = r12698788 + r12698789;
        return r12698790;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r12698791 = z;
        double r12698792 = t;
        double r12698793 = 16.0;
        double r12698794 = r12698792 / r12698793;
        double r12698795 = r12698791 * r12698794;
        double r12698796 = x;
        double r12698797 = y;
        double r12698798 = r12698796 * r12698797;
        double r12698799 = r12698795 + r12698798;
        double r12698800 = a;
        double r12698801 = b;
        double r12698802 = r12698800 * r12698801;
        double r12698803 = 4.0;
        double r12698804 = r12698802 / r12698803;
        double r12698805 = r12698799 - r12698804;
        double r12698806 = c;
        double r12698807 = r12698805 + r12698806;
        return r12698807;
}

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 2019165 
(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))