Average Error: 0.1 → 0.1
Time: 4.7s
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 r220343 = 1.0;
        double r220344 = 2.0;
        double r220345 = r220343 / r220344;
        double r220346 = x;
        double r220347 = y;
        double r220348 = z;
        double r220349 = sqrt(r220348);
        double r220350 = r220347 * r220349;
        double r220351 = r220346 + r220350;
        double r220352 = r220345 * r220351;
        return r220352;
}
↓
double f(double x, double y, double z) {
        double r220353 = 1.0;
        double r220354 = 2.0;
        double r220355 = r220353 / r220354;
        double r220356 = x;
        double r220357 = y;
        double r220358 = z;
        double r220359 = sqrt(r220358);
        double r220360 = r220357 * r220359;
        double r220361 = r220356 + r220360;
        double r220362 = r220355 * r220361;
        return r220362;
}

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 2020034 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))