Average Error: 0.1 → 0.1
Time: 17.5s
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 r7232162 = 1.0;
        double r7232163 = 2.0;
        double r7232164 = r7232162 / r7232163;
        double r7232165 = x;
        double r7232166 = y;
        double r7232167 = z;
        double r7232168 = sqrt(r7232167);
        double r7232169 = r7232166 * r7232168;
        double r7232170 = r7232165 + r7232169;
        double r7232171 = r7232164 * r7232170;
        return r7232171;
}
↓
double f(double x, double y, double z) {
        double r7232172 = 1.0;
        double r7232173 = 2.0;
        double r7232174 = r7232172 / r7232173;
        double r7232175 = x;
        double r7232176 = z;
        double r7232177 = sqrt(r7232176);
        double r7232178 = y;
        double r7232179 = r7232177 * r7232178;
        double r7232180 = r7232175 + r7232179;
        double r7232181 = r7232174 * r7232180;
        return r7232181;
}

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 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))