Average Error: 0.1 → 0.1
Time: 15.9s
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 r14269480 = 1.0;
        double r14269481 = 2.0;
        double r14269482 = r14269480 / r14269481;
        double r14269483 = x;
        double r14269484 = y;
        double r14269485 = z;
        double r14269486 = sqrt(r14269485);
        double r14269487 = r14269484 * r14269486;
        double r14269488 = r14269483 + r14269487;
        double r14269489 = r14269482 * r14269488;
        return r14269489;
}
↓
double f(double x, double y, double z) {
        double r14269490 = 1.0;
        double r14269491 = 2.0;
        double r14269492 = r14269490 / r14269491;
        double r14269493 = x;
        double r14269494 = r14269492 * r14269493;
        double r14269495 = y;
        double r14269496 = r14269492 * r14269495;
        double r14269497 = z;
        double r14269498 = sqrt(r14269497);
        double r14269499 = r14269496 * r14269498;
        double r14269500 = r14269494 + r14269499;
        return r14269500;
}

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-rgt-in0.3

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

  8. Simplified0.1

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

  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)))))