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 r237230 = 1.0;
        double r237231 = 2.0;
        double r237232 = r237230 / r237231;
        double r237233 = x;
        double r237234 = y;
        double r237235 = z;
        double r237236 = sqrt(r237235);
        double r237237 = r237234 * r237236;
        double r237238 = r237233 + r237237;
        double r237239 = r237232 * r237238;
        return r237239;
}
↓
double f(double x, double y, double z) {
        double r237240 = 1.0;
        double r237241 = 2.0;
        double r237242 = r237240 / r237241;
        double r237243 = x;
        double r237244 = r237242 * r237243;
        double r237245 = y;
        double r237246 = r237242 * r237245;
        double r237247 = z;
        double r237248 = sqrt(r237247);
        double r237249 = r237246 * r237248;
        double r237250 = r237244 + r237249;
        return r237250;
}

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)))))