Average Error: 0.2 → 0.0
Time: 22.5s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(z \cdot \frac{t}{16} + x \cdot y\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(z \cdot \frac{t}{16} + x \cdot y\right) - \frac{a \cdot b}{4}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r13069605 = x;
        double r13069606 = y;
        double r13069607 = r13069605 * r13069606;
        double r13069608 = z;
        double r13069609 = t;
        double r13069610 = r13069608 * r13069609;
        double r13069611 = 16.0;
        double r13069612 = r13069610 / r13069611;
        double r13069613 = r13069607 + r13069612;
        double r13069614 = a;
        double r13069615 = b;
        double r13069616 = r13069614 * r13069615;
        double r13069617 = 4.0;
        double r13069618 = r13069616 / r13069617;
        double r13069619 = r13069613 - r13069618;
        double r13069620 = c;
        double r13069621 = r13069619 + r13069620;
        return r13069621;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r13069622 = z;
        double r13069623 = t;
        double r13069624 = 16.0;
        double r13069625 = r13069623 / r13069624;
        double r13069626 = r13069622 * r13069625;
        double r13069627 = x;
        double r13069628 = y;
        double r13069629 = r13069627 * r13069628;
        double r13069630 = r13069626 + r13069629;
        double r13069631 = a;
        double r13069632 = b;
        double r13069633 = r13069631 * r13069632;
        double r13069634 = 4.0;
        double r13069635 = r13069633 / r13069634;
        double r13069636 = r13069630 - r13069635;
        double r13069637 = c;
        double r13069638 = r13069636 + r13069637;
        return r13069638;
}

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 0.2

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

  3. Applied *-un-lft-identity0.2

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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))