Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
double f(double x, double y, double z) {
        double r330205 = 1.0;
        double r330206 = 2.0;
        double r330207 = r330205 / r330206;
        double r330208 = x;
        double r330209 = y;
        double r330210 = z;
        double r330211 = sqrt(r330210);
        double r330212 = r330209 * r330211;
        double r330213 = r330208 + r330212;
        double r330214 = r330207 * r330213;
        return r330214;
}
↓
double f(double x, double y, double z) {
        double r330215 = 1.0;
        double r330216 = 2.0;
        double r330217 = r330215 / r330216;
        double r330218 = x;
        double r330219 = y;
        double r330220 = z;
        double r330221 = sqrt(r330220);
        double r330222 = r330219 * r330221;
        double r330223 = r330218 + r330222;
        double r330224 = r330217 * r330223;
        return r330224;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))