Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\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 r11776324 = 1.0;
        double r11776325 = 2.0;
        double r11776326 = r11776324 / r11776325;
        double r11776327 = x;
        double r11776328 = y;
        double r11776329 = z;
        double r11776330 = sqrt(r11776329);
        double r11776331 = r11776328 * r11776330;
        double r11776332 = r11776327 + r11776331;
        double r11776333 = r11776326 * r11776332;
        return r11776333;
}
↓
double f(double x, double y, double z) {
        double r11776334 = 1.0;
        double r11776335 = 2.0;
        double r11776336 = r11776334 / r11776335;
        double r11776337 = x;
        double r11776338 = z;
        double r11776339 = sqrt(r11776338);
        double r11776340 = y;
        double r11776341 = r11776339 * r11776340;
        double r11776342 = r11776337 + r11776341;
        double r11776343 = r11776336 * r11776342;
        return r11776343;
}

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)))))