Average Error: 0.1 → 0.1
Time: 19.5s
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 r147544 = 1.0;
        double r147545 = 2.0;
        double r147546 = r147544 / r147545;
        double r147547 = x;
        double r147548 = y;
        double r147549 = z;
        double r147550 = sqrt(r147549);
        double r147551 = r147548 * r147550;
        double r147552 = r147547 + r147551;
        double r147553 = r147546 * r147552;
        return r147553;
}
↓
double f(double x, double y, double z) {
        double r147554 = 1.0;
        double r147555 = 2.0;
        double r147556 = r147554 / r147555;
        double r147557 = x;
        double r147558 = y;
        double r147559 = z;
        double r147560 = sqrt(r147559);
        double r147561 = r147558 * r147560;
        double r147562 = r147557 + r147561;
        double r147563 = r147556 * r147562;
        return r147563;
}

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 2019323 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))