Average Error: 0.1 → 0.1
Time: 4.1s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{\left(\sqrt{z} \cdot y + x\right) \cdot 1}{2}\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{\left(\sqrt{z} \cdot y + x\right) \cdot 1}{2}
double f(double x, double y, double z) {
        double r192072 = 1.0;
        double r192073 = 2.0;
        double r192074 = r192072 / r192073;
        double r192075 = x;
        double r192076 = y;
        double r192077 = z;
        double r192078 = sqrt(r192077);
        double r192079 = r192076 * r192078;
        double r192080 = r192075 + r192079;
        double r192081 = r192074 * r192080;
        return r192081;
}
↓
double f(double x, double y, double z) {
        double r192082 = z;
        double r192083 = sqrt(r192082);
        double r192084 = y;
        double r192085 = r192083 * r192084;
        double r192086 = x;
        double r192087 = r192085 + r192086;
        double r192088 = 1.0;
        double r192089 = r192087 * r192088;
        double r192090 = 2.0;
        double r192091 = r192089 / r192090;
        return r192091;
}

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

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\sqrt{z}, y, x\right) \cdot 1}{2}}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))