Average Error: 0.1 → 0.1
Time: 18.8s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r11045425 = 1.0;
        double r11045426 = 2.0;
        double r11045427 = r11045425 / r11045426;
        double r11045428 = x;
        double r11045429 = y;
        double r11045430 = z;
        double r11045431 = sqrt(r11045430);
        double r11045432 = r11045429 * r11045431;
        double r11045433 = r11045428 + r11045432;
        double r11045434 = r11045427 * r11045433;
        return r11045434;
}
↓
double f(double x, double y, double z) {
        double r11045435 = 1.0;
        double r11045436 = 2.0;
        double r11045437 = r11045435 / r11045436;
        double r11045438 = x;
        double r11045439 = z;
        double r11045440 = sqrt(r11045439);
        double r11045441 = y;
        double r11045442 = r11045440 * r11045441;
        double r11045443 = r11045438 + r11045442;
        double r11045444 = r11045437 * r11045443;
        return r11045444;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))