Average Error: 0.1 → 0.1
Time: 17.6s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r11572693 = 1.0;
        double r11572694 = 2.0;
        double r11572695 = r11572693 / r11572694;
        double r11572696 = x;
        double r11572697 = y;
        double r11572698 = z;
        double r11572699 = sqrt(r11572698);
        double r11572700 = r11572697 * r11572699;
        double r11572701 = r11572696 + r11572700;
        double r11572702 = r11572695 * r11572701;
        return r11572702;
}
↓
double f(double x, double y, double z) {
        double r11572703 = 1.0;
        double r11572704 = 2.0;
        double r11572705 = r11572703 / r11572704;
        double r11572706 = x;
        double r11572707 = z;
        double r11572708 = sqrt(r11572707);
        double r11572709 = y;
        double r11572710 = r11572708 * r11572709;
        double r11572711 = r11572706 + r11572710;
        double r11572712 = r11572705 * r11572711;
        return r11572712;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))