Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot x + \left(\frac{1}{2} \cdot y\right) \cdot \sqrt{z}\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot x + \left(\frac{1}{2} \cdot y\right) \cdot \sqrt{z}
double f(double x, double y, double z) {
        double r214049 = 1.0;
        double r214050 = 2.0;
        double r214051 = r214049 / r214050;
        double r214052 = x;
        double r214053 = y;
        double r214054 = z;
        double r214055 = sqrt(r214054);
        double r214056 = r214053 * r214055;
        double r214057 = r214052 + r214056;
        double r214058 = r214051 * r214057;
        return r214058;
}
↓
double f(double x, double y, double z) {
        double r214059 = 1.0;
        double r214060 = 2.0;
        double r214061 = r214059 / r214060;
        double r214062 = x;
        double r214063 = r214061 * r214062;
        double r214064 = y;
        double r214065 = r214061 * r214064;
        double r214066 = z;
        double r214067 = sqrt(r214066);
        double r214068 = r214065 * r214067;
        double r214069 = r214063 + r214068;
        return r214069;
}

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

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.3

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

  5. Applied associate-*r*0.3

    \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{\left(y \cdot \sqrt{\sqrt{z}}\right) \cdot \sqrt{\sqrt{z}}}\right)\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.3

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))