Average Error: 0.2 → 0.1
Time: 14.2s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[x \cdot \frac{1}{2} + \left(\frac{1}{2} \cdot \sqrt{z}\right) \cdot y\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
x \cdot \frac{1}{2} + \left(\frac{1}{2} \cdot \sqrt{z}\right) \cdot y
double f(double x, double y, double z) {
        double r219604 = 1.0;
        double r219605 = 2.0;
        double r219606 = r219604 / r219605;
        double r219607 = x;
        double r219608 = y;
        double r219609 = z;
        double r219610 = sqrt(r219609);
        double r219611 = r219608 * r219610;
        double r219612 = r219607 + r219611;
        double r219613 = r219606 * r219612;
        return r219613;
}
↓
double f(double x, double y, double z) {
        double r219614 = x;
        double r219615 = 1.0;
        double r219616 = 2.0;
        double r219617 = r219615 / r219616;
        double r219618 = r219614 * r219617;
        double r219619 = z;
        double r219620 = sqrt(r219619);
        double r219621 = r219617 * r219620;
        double r219622 = y;
        double r219623 = r219621 * r219622;
        double r219624 = r219618 + r219623;
        return r219624;
}

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 0.2

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

  3. Applied add-sqr-sqrt1.3

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

  4. Applied associate-*l*1.0

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

  6. Applied distribute-lft-in0.9

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

  7. Applied distribute-lft-in1.0

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

  8. Simplified0.5

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))