Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}
double f(double x, double y, double z) {
        double r234301 = 1.0;
        double r234302 = 2.0;
        double r234303 = r234301 / r234302;
        double r234304 = x;
        double r234305 = y;
        double r234306 = z;
        double r234307 = sqrt(r234306);
        double r234308 = r234305 * r234307;
        double r234309 = r234304 + r234308;
        double r234310 = r234303 * r234309;
        return r234310;
}
↓
double f(double x, double y, double z) {
        double r234311 = 1.0;
        double r234312 = x;
        double r234313 = z;
        double r234314 = sqrt(r234313);
        double r234315 = y;
        double r234316 = r234314 * r234315;
        double r234317 = r234312 + r234316;
        double r234318 = r234311 * r234317;
        double r234319 = 2.0;
        double r234320 = r234318 / r234319;
        return r234320;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))