Average Error: 0.1 → 0.1
Time: 16.1s
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 r167102 = 1.0;
        double r167103 = 2.0;
        double r167104 = r167102 / r167103;
        double r167105 = x;
        double r167106 = y;
        double r167107 = z;
        double r167108 = sqrt(r167107);
        double r167109 = r167106 * r167108;
        double r167110 = r167105 + r167109;
        double r167111 = r167104 * r167110;
        return r167111;
}
↓
double f(double x, double y, double z) {
        double r167112 = 1.0;
        double r167113 = 2.0;
        double r167114 = r167112 / r167113;
        double r167115 = x;
        double r167116 = y;
        double r167117 = z;
        double r167118 = sqrt(r167117);
        double r167119 = r167116 * r167118;
        double r167120 = r167115 + r167119;
        double r167121 = r167114 * r167120;
        return r167121;
}

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