Average Error: 0.2 → 0.2
Time: 10.4s
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 r263341 = 1.0;
        double r263342 = 2.0;
        double r263343 = r263341 / r263342;
        double r263344 = x;
        double r263345 = y;
        double r263346 = z;
        double r263347 = sqrt(r263346);
        double r263348 = r263345 * r263347;
        double r263349 = r263344 + r263348;
        double r263350 = r263343 * r263349;
        return r263350;
}
↓
double f(double x, double y, double z) {
        double r263351 = 1.0;
        double r263352 = 2.0;
        double r263353 = r263351 / r263352;
        double r263354 = x;
        double r263355 = y;
        double r263356 = z;
        double r263357 = sqrt(r263356);
        double r263358 = r263355 * r263357;
        double r263359 = r263354 + r263358;
        double r263360 = r263353 * r263359;
        return r263360;
}

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 2020047 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))