Average Error: 0.1 → 0.1
Time: 15.7s
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 r9049210 = 1.0;
        double r9049211 = 2.0;
        double r9049212 = r9049210 / r9049211;
        double r9049213 = x;
        double r9049214 = y;
        double r9049215 = z;
        double r9049216 = sqrt(r9049215);
        double r9049217 = r9049214 * r9049216;
        double r9049218 = r9049213 + r9049217;
        double r9049219 = r9049212 * r9049218;
        return r9049219;
}
↓
double f(double x, double y, double z) {
        double r9049220 = 1.0;
        double r9049221 = 2.0;
        double r9049222 = r9049220 / r9049221;
        double r9049223 = x;
        double r9049224 = r9049222 * r9049223;
        double r9049225 = y;
        double r9049226 = r9049222 * r9049225;
        double r9049227 = z;
        double r9049228 = sqrt(r9049227);
        double r9049229 = r9049226 * r9049228;
        double r9049230 = r9049224 + r9049229;
        return r9049230;
}

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 2019172 +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)))))