Average Error: 0.2 → 0.2
Time: 15.2s
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 r10670943 = 1.0;
        double r10670944 = 2.0;
        double r10670945 = r10670943 / r10670944;
        double r10670946 = x;
        double r10670947 = y;
        double r10670948 = z;
        double r10670949 = sqrt(r10670948);
        double r10670950 = r10670947 * r10670949;
        double r10670951 = r10670946 + r10670950;
        double r10670952 = r10670945 * r10670951;
        return r10670952;
}
↓
double f(double x, double y, double z) {
        double r10670953 = 1.0;
        double r10670954 = 2.0;
        double r10670955 = r10670953 / r10670954;
        double r10670956 = x;
        double r10670957 = z;
        double r10670958 = sqrt(r10670957);
        double r10670959 = y;
        double r10670960 = r10670958 * r10670959;
        double r10670961 = r10670956 + r10670960;
        double r10670962 = r10670955 * r10670961;
        return r10670962;
}

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 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))