Average Error: 0.2 → 0.2
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 r248404 = 1.0;
        double r248405 = 2.0;
        double r248406 = r248404 / r248405;
        double r248407 = x;
        double r248408 = y;
        double r248409 = z;
        double r248410 = sqrt(r248409);
        double r248411 = r248408 * r248410;
        double r248412 = r248407 + r248411;
        double r248413 = r248406 * r248412;
        return r248413;
}
↓
double f(double x, double y, double z) {
        double r248414 = 1.0;
        double r248415 = 2.0;
        double r248416 = r248414 / r248415;
        double r248417 = x;
        double r248418 = y;
        double r248419 = z;
        double r248420 = sqrt(r248419);
        double r248421 = r248418 * r248420;
        double r248422 = r248417 + r248421;
        double r248423 = r248416 * r248422;
        return r248423;
}

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 2020064 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))