Average Error: 0.1 → 0.1
Time: 14.3s
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 r143589 = 1.0;
        double r143590 = 2.0;
        double r143591 = r143589 / r143590;
        double r143592 = x;
        double r143593 = y;
        double r143594 = z;
        double r143595 = sqrt(r143594);
        double r143596 = r143593 * r143595;
        double r143597 = r143592 + r143596;
        double r143598 = r143591 * r143597;
        return r143598;
}
↓
double f(double x, double y, double z) {
        double r143599 = 1.0;
        double r143600 = 2.0;
        double r143601 = r143599 / r143600;
        double r143602 = x;
        double r143603 = y;
        double r143604 = z;
        double r143605 = sqrt(r143604);
        double r143606 = r143603 * r143605;
        double r143607 = r143602 + r143606;
        double r143608 = r143601 * r143607;
        return r143608;
}

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 2019198 +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)))))