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 r185938 = 1.0;
        double r185939 = 2.0;
        double r185940 = r185938 / r185939;
        double r185941 = x;
        double r185942 = y;
        double r185943 = z;
        double r185944 = sqrt(r185943);
        double r185945 = r185942 * r185944;
        double r185946 = r185941 + r185945;
        double r185947 = r185940 * r185946;
        return r185947;
}
↓
double f(double x, double y, double z) {
        double r185948 = z;
        double r185949 = sqrt(r185948);
        double r185950 = y;
        double r185951 = r185949 * r185950;
        double r185952 = x;
        double r185953 = r185951 + r185952;
        double r185954 = 1.0;
        double r185955 = r185953 * r185954;
        double r185956 = 2.0;
        double r185957 = r185955 / r185956;
        return r185957;
}

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)))))