Average Error: 0.1 → 0.1
Time: 4.4s
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 r202487 = 1.0;
        double r202488 = 2.0;
        double r202489 = r202487 / r202488;
        double r202490 = x;
        double r202491 = y;
        double r202492 = z;
        double r202493 = sqrt(r202492);
        double r202494 = r202491 * r202493;
        double r202495 = r202490 + r202494;
        double r202496 = r202489 * r202495;
        return r202496;
}
↓
double f(double x, double y, double z) {
        double r202497 = 1.0;
        double r202498 = 2.0;
        double r202499 = r202497 / r202498;
        double r202500 = x;
        double r202501 = y;
        double r202502 = z;
        double r202503 = sqrt(r202502);
        double r202504 = r202501 * r202503;
        double r202505 = r202500 + r202504;
        double r202506 = r202499 * r202505;
        return r202506;
}

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 2019362 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))