Average Error: 0.2 → 0.2
Time: 13.5s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(y \cdot \sqrt{z} + x\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(y \cdot \sqrt{z} + x\right)
double f(double x, double y, double z) {
        double r13771810 = 1.0;
        double r13771811 = 2.0;
        double r13771812 = r13771810 / r13771811;
        double r13771813 = x;
        double r13771814 = y;
        double r13771815 = z;
        double r13771816 = sqrt(r13771815);
        double r13771817 = r13771814 * r13771816;
        double r13771818 = r13771813 + r13771817;
        double r13771819 = r13771812 * r13771818;
        return r13771819;
}
↓
double f(double x, double y, double z) {
        double r13771820 = 1.0;
        double r13771821 = 2.0;
        double r13771822 = r13771820 / r13771821;
        double r13771823 = y;
        double r13771824 = z;
        double r13771825 = sqrt(r13771824);
        double r13771826 = r13771823 * r13771825;
        double r13771827 = x;
        double r13771828 = r13771826 + r13771827;
        double r13771829 = r13771822 * r13771828;
        return r13771829;
}

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 0.2

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
  2. Using strategy rm

  3. Applied +-commutative0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))