Average Error: 0.1 → 0.1
Time: 16.6s
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 r12014010 = 1.0;
        double r12014011 = 2.0;
        double r12014012 = r12014010 / r12014011;
        double r12014013 = x;
        double r12014014 = y;
        double r12014015 = z;
        double r12014016 = sqrt(r12014015);
        double r12014017 = r12014014 * r12014016;
        double r12014018 = r12014013 + r12014017;
        double r12014019 = r12014012 * r12014018;
        return r12014019;
}
↓
double f(double x, double y, double z) {
        double r12014020 = 1.0;
        double r12014021 = 2.0;
        double r12014022 = r12014020 / r12014021;
        double r12014023 = x;
        double r12014024 = z;
        double r12014025 = sqrt(r12014024);
        double r12014026 = y;
        double r12014027 = r12014025 * r12014026;
        double r12014028 = r12014023 + r12014027;
        double r12014029 = r12014022 * r12014028;
        return r12014029;
}

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)))))