Average Error: 0.1 → 0.1
Time: 5.5s
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 r338198 = 1.0;
        double r338199 = 2.0;
        double r338200 = r338198 / r338199;
        double r338201 = x;
        double r338202 = y;
        double r338203 = z;
        double r338204 = sqrt(r338203);
        double r338205 = r338202 * r338204;
        double r338206 = r338201 + r338205;
        double r338207 = r338200 * r338206;
        return r338207;
}
↓
double f(double x, double y, double z) {
        double r338208 = 1.0;
        double r338209 = 2.0;
        double r338210 = r338208 / r338209;
        double r338211 = x;
        double r338212 = y;
        double r338213 = z;
        double r338214 = sqrt(r338213);
        double r338215 = r338212 * r338214;
        double r338216 = r338211 + r338215;
        double r338217 = r338210 * r338216;
        return r338217;
}

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 2020035 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))