Average Error: 0.1 → 0.1
Time: 16.0s
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 r7770306 = 1.0;
        double r7770307 = 2.0;
        double r7770308 = r7770306 / r7770307;
        double r7770309 = x;
        double r7770310 = y;
        double r7770311 = z;
        double r7770312 = sqrt(r7770311);
        double r7770313 = r7770310 * r7770312;
        double r7770314 = r7770309 + r7770313;
        double r7770315 = r7770308 * r7770314;
        return r7770315;
}
↓
double f(double x, double y, double z) {
        double r7770316 = 1.0;
        double r7770317 = 2.0;
        double r7770318 = r7770316 / r7770317;
        double r7770319 = x;
        double r7770320 = z;
        double r7770321 = sqrt(r7770320);
        double r7770322 = y;
        double r7770323 = r7770321 * r7770322;
        double r7770324 = r7770319 + r7770323;
        double r7770325 = r7770318 * r7770324;
        return r7770325;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))