Average Error: 0.1 → 0.1
Time: 17.3s
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 r20131008 = 1.0;
        double r20131009 = 2.0;
        double r20131010 = r20131008 / r20131009;
        double r20131011 = x;
        double r20131012 = y;
        double r20131013 = z;
        double r20131014 = sqrt(r20131013);
        double r20131015 = r20131012 * r20131014;
        double r20131016 = r20131011 + r20131015;
        double r20131017 = r20131010 * r20131016;
        return r20131017;
}
↓
double f(double x, double y, double z) {
        double r20131018 = 1.0;
        double r20131019 = 2.0;
        double r20131020 = r20131018 / r20131019;
        double r20131021 = x;
        double r20131022 = z;
        double r20131023 = sqrt(r20131022);
        double r20131024 = y;
        double r20131025 = r20131023 * r20131024;
        double r20131026 = r20131021 + r20131025;
        double r20131027 = r20131020 * r20131026;
        return r20131027;
}

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)))))