Average Error: 0.2 → 0.2
Time: 13.5s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r9299944 = 1.0;
        double r9299945 = 2.0;
        double r9299946 = r9299944 / r9299945;
        double r9299947 = x;
        double r9299948 = y;
        double r9299949 = z;
        double r9299950 = sqrt(r9299949);
        double r9299951 = r9299948 * r9299950;
        double r9299952 = r9299947 + r9299951;
        double r9299953 = r9299946 * r9299952;
        return r9299953;
}
↓
double f(double x, double y, double z) {
        double r9299954 = 1.0;
        double r9299955 = 2.0;
        double r9299956 = r9299954 / r9299955;
        double r9299957 = x;
        double r9299958 = z;
        double r9299959 = sqrt(r9299958);
        double r9299960 = y;
        double r9299961 = r9299959 * r9299960;
        double r9299962 = r9299957 + r9299961;
        double r9299963 = r9299956 * r9299962;
        return r9299963;
}

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

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.2

    \[\leadsto \frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019174 +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)))))