Average Error: 0.2 → 0.2
Time: 19.5s
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 r163336 = 1.0;
        double r163337 = 2.0;
        double r163338 = r163336 / r163337;
        double r163339 = x;
        double r163340 = y;
        double r163341 = z;
        double r163342 = sqrt(r163341);
        double r163343 = r163340 * r163342;
        double r163344 = r163339 + r163343;
        double r163345 = r163338 * r163344;
        return r163345;
}
↓
double f(double x, double y, double z) {
        double r163346 = 1.0;
        double r163347 = 2.0;
        double r163348 = r163346 / r163347;
        double r163349 = x;
        double r163350 = y;
        double r163351 = z;
        double r163352 = sqrt(r163351);
        double r163353 = r163350 * r163352;
        double r163354 = r163349 + r163353;
        double r163355 = r163348 * r163354;
        return r163355;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))