Average Error: 0.1 → 0.1
Time: 3.4s
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 r225159 = 1.0;
        double r225160 = 2.0;
        double r225161 = r225159 / r225160;
        double r225162 = x;
        double r225163 = y;
        double r225164 = z;
        double r225165 = sqrt(r225164);
        double r225166 = r225163 * r225165;
        double r225167 = r225162 + r225166;
        double r225168 = r225161 * r225167;
        return r225168;
}
↓
double f(double x, double y, double z) {
        double r225169 = 1.0;
        double r225170 = 2.0;
        double r225171 = r225169 / r225170;
        double r225172 = x;
        double r225173 = r225171 * r225172;
        double r225174 = y;
        double r225175 = r225171 * r225174;
        double r225176 = z;
        double r225177 = sqrt(r225176);
        double r225178 = r225175 * r225177;
        double r225179 = r225173 + r225178;
        return r225179;
}

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 2020024 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))