Average Error: 0.2 → 0.2
Time: 10.2s
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 r3732269 = 1.0;
        double r3732270 = 2.0;
        double r3732271 = r3732269 / r3732270;
        double r3732272 = x;
        double r3732273 = y;
        double r3732274 = z;
        double r3732275 = sqrt(r3732274);
        double r3732276 = r3732273 * r3732275;
        double r3732277 = r3732272 + r3732276;
        double r3732278 = r3732271 * r3732277;
        return r3732278;
}
↓
double f(double x, double y, double z) {
        double r3732279 = 1.0;
        double r3732280 = 2.0;
        double r3732281 = r3732279 / r3732280;
        double r3732282 = x;
        double r3732283 = z;
        double r3732284 = sqrt(r3732283);
        double r3732285 = y;
        double r3732286 = r3732284 * r3732285;
        double r3732287 = r3732282 + r3732286;
        double r3732288 = r3732281 * r3732287;
        return r3732288;
}

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))