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 r235447 = 1.0;
        double r235448 = 2.0;
        double r235449 = r235447 / r235448;
        double r235450 = x;
        double r235451 = y;
        double r235452 = z;
        double r235453 = sqrt(r235452);
        double r235454 = r235451 * r235453;
        double r235455 = r235450 + r235454;
        double r235456 = r235449 * r235455;
        return r235456;
}
↓
double f(double x, double y, double z) {
        double r235457 = 1.0;
        double r235458 = 2.0;
        double r235459 = r235457 / r235458;
        double r235460 = x;
        double r235461 = y;
        double r235462 = z;
        double r235463 = sqrt(r235462);
        double r235464 = r235461 * r235463;
        double r235465 = r235460 + r235464;
        double r235466 = r235459 * r235465;
        return r235466;
}

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 2020018 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))