Average Error: 0.2 → 0.2
Time: 18.8s
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 r176661 = 1.0;
        double r176662 = 2.0;
        double r176663 = r176661 / r176662;
        double r176664 = x;
        double r176665 = y;
        double r176666 = z;
        double r176667 = sqrt(r176666);
        double r176668 = r176665 * r176667;
        double r176669 = r176664 + r176668;
        double r176670 = r176663 * r176669;
        return r176670;
}
↓
double f(double x, double y, double z) {
        double r176671 = 1.0;
        double r176672 = 2.0;
        double r176673 = r176671 / r176672;
        double r176674 = x;
        double r176675 = y;
        double r176676 = z;
        double r176677 = sqrt(r176676);
        double r176678 = r176675 * r176677;
        double r176679 = r176674 + r176678;
        double r176680 = r176673 * r176679;
        return r176680;
}

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 2019325 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))