Average Error: 0.1 → 0.1
Time: 34.4s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r14163304 = 1.0;
        double r14163305 = 2.0;
        double r14163306 = r14163304 / r14163305;
        double r14163307 = x;
        double r14163308 = y;
        double r14163309 = z;
        double r14163310 = sqrt(r14163309);
        double r14163311 = r14163308 * r14163310;
        double r14163312 = r14163307 + r14163311;
        double r14163313 = r14163306 * r14163312;
        return r14163313;
}
↓
double f(double x, double y, double z) {
        double r14163314 = 1.0;
        double r14163315 = 2.0;
        double r14163316 = r14163314 / r14163315;
        double r14163317 = x;
        double r14163318 = z;
        double r14163319 = sqrt(r14163318);
        double r14163320 = y;
        double r14163321 = r14163319 * r14163320;
        double r14163322 = r14163317 + r14163321;
        double r14163323 = r14163316 * r14163322;
        return r14163323;
}

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

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))