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 r166042 = 1.0;
        double r166043 = 2.0;
        double r166044 = r166042 / r166043;
        double r166045 = x;
        double r166046 = y;
        double r166047 = z;
        double r166048 = sqrt(r166047);
        double r166049 = r166046 * r166048;
        double r166050 = r166045 + r166049;
        double r166051 = r166044 * r166050;
        return r166051;
}
↓
double f(double x, double y, double z) {
        double r166052 = 1.0;
        double r166053 = x;
        double r166054 = z;
        double r166055 = sqrt(r166054);
        double r166056 = y;
        double r166057 = r166055 * r166056;
        double r166058 = r166053 + r166057;
        double r166059 = r166052 * r166058;
        double r166060 = 2.0;
        double r166061 = r166059 / r166060;
        return r166061;
}

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 2019196 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))