Average Error: 0.1 → 0.1
Time: 19.3s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r12993648 = 1.0;
        double r12993649 = 2.0;
        double r12993650 = r12993648 / r12993649;
        double r12993651 = x;
        double r12993652 = y;
        double r12993653 = z;
        double r12993654 = sqrt(r12993653);
        double r12993655 = r12993652 * r12993654;
        double r12993656 = r12993651 + r12993655;
        double r12993657 = r12993650 * r12993656;
        return r12993657;
}
↓
double f(double x, double y, double z) {
        double r12993658 = 1.0;
        double r12993659 = 2.0;
        double r12993660 = r12993658 / r12993659;
        double r12993661 = x;
        double r12993662 = z;
        double r12993663 = sqrt(r12993662);
        double r12993664 = y;
        double r12993665 = r12993663 * r12993664;
        double r12993666 = r12993661 + r12993665;
        double r12993667 = r12993660 * r12993666;
        return r12993667;
}

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

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))