Average Error: 0.1 → 0.1
Time: 13.0s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot x + \left(\frac{1}{2} \cdot \sqrt{z}\right) \cdot y\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot x + \left(\frac{1}{2} \cdot \sqrt{z}\right) \cdot y
double f(double x, double y, double z) {
        double r8377522 = 1.0;
        double r8377523 = 2.0;
        double r8377524 = r8377522 / r8377523;
        double r8377525 = x;
        double r8377526 = y;
        double r8377527 = z;
        double r8377528 = sqrt(r8377527);
        double r8377529 = r8377526 * r8377528;
        double r8377530 = r8377525 + r8377529;
        double r8377531 = r8377524 * r8377530;
        return r8377531;
}
↓
double f(double x, double y, double z) {
        double r8377532 = 1.0;
        double r8377533 = 2.0;
        double r8377534 = r8377532 / r8377533;
        double r8377535 = x;
        double r8377536 = r8377534 * r8377535;
        double r8377537 = z;
        double r8377538 = sqrt(r8377537);
        double r8377539 = r8377534 * r8377538;
        double r8377540 = y;
        double r8377541 = r8377539 * r8377540;
        double r8377542 = r8377536 + r8377541;
        return r8377542;
}

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

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

  9. Final simplification0.1

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

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)))))