Average Error: 0.1 → 0.1
Time: 4.8s
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 r238016 = 1.0;
        double r238017 = 2.0;
        double r238018 = r238016 / r238017;
        double r238019 = x;
        double r238020 = y;
        double r238021 = z;
        double r238022 = sqrt(r238021);
        double r238023 = r238020 * r238022;
        double r238024 = r238019 + r238023;
        double r238025 = r238018 * r238024;
        return r238025;
}
↓
double f(double x, double y, double z) {
        double r238026 = 1.0;
        double r238027 = 2.0;
        double r238028 = r238026 / r238027;
        double r238029 = x;
        double r238030 = y;
        double r238031 = z;
        double r238032 = sqrt(r238031);
        double r238033 = r238030 * r238032;
        double r238034 = r238029 + r238033;
        double r238035 = r238028 * r238034;
        return r238035;
}

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 2020100 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))