Average Error: 0.1 → 0.1
Time: 25.0s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\left(\left(\frac{z}{\frac{16.0}{t}} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\left(\left(\frac{z}{\frac{16.0}{t}} + 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 r9387653 = x;
        double r9387654 = y;
        double r9387655 = r9387653 * r9387654;
        double r9387656 = z;
        double r9387657 = t;
        double r9387658 = r9387656 * r9387657;
        double r9387659 = 16.0;
        double r9387660 = r9387658 / r9387659;
        double r9387661 = r9387655 + r9387660;
        double r9387662 = a;
        double r9387663 = b;
        double r9387664 = r9387662 * r9387663;
        double r9387665 = 4.0;
        double r9387666 = r9387664 / r9387665;
        double r9387667 = r9387661 - r9387666;
        double r9387668 = c;
        double r9387669 = r9387667 + r9387668;
        return r9387669;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9387670 = z;
        double r9387671 = 16.0;
        double r9387672 = t;
        double r9387673 = r9387671 / r9387672;
        double r9387674 = r9387670 / r9387673;
        double r9387675 = x;
        double r9387676 = y;
        double r9387677 = r9387675 * r9387676;
        double r9387678 = r9387674 + r9387677;
        double r9387679 = a;
        double r9387680 = b;
        double r9387681 = r9387679 * r9387680;
        double r9387682 = 4.0;
        double r9387683 = r9387681 / r9387682;
        double r9387684 = r9387678 - r9387683;
        double r9387685 = c;
        double r9387686 = r9387684 + r9387685;
        return r9387686;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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))