Average Error: 0.1 → 0.1
Time: 5.0s
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 r235170 = 1.0;
        double r235171 = 2.0;
        double r235172 = r235170 / r235171;
        double r235173 = x;
        double r235174 = y;
        double r235175 = z;
        double r235176 = sqrt(r235175);
        double r235177 = r235174 * r235176;
        double r235178 = r235173 + r235177;
        double r235179 = r235172 * r235178;
        return r235179;
}
↓
double f(double x, double y, double z) {
        double r235180 = 1.0;
        double r235181 = 2.0;
        double r235182 = r235180 / r235181;
        double r235183 = x;
        double r235184 = y;
        double r235185 = z;
        double r235186 = sqrt(r235185);
        double r235187 = r235184 * r235186;
        double r235188 = r235183 + r235187;
        double r235189 = r235182 * r235188;
        return r235189;
}

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 2019362 +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)))))