Average Error: 0.1 → 0.1
Time: 8.8s
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 r176213 = 1.0;
        double r176214 = 2.0;
        double r176215 = r176213 / r176214;
        double r176216 = x;
        double r176217 = y;
        double r176218 = z;
        double r176219 = sqrt(r176218);
        double r176220 = r176217 * r176219;
        double r176221 = r176216 + r176220;
        double r176222 = r176215 * r176221;
        return r176222;
}
↓
double f(double x, double y, double z) {
        double r176223 = 1.0;
        double r176224 = 2.0;
        double r176225 = r176223 / r176224;
        double r176226 = x;
        double r176227 = y;
        double r176228 = z;
        double r176229 = sqrt(r176228);
        double r176230 = r176227 * r176229;
        double r176231 = r176226 + r176230;
        double r176232 = r176225 * r176231;
        return r176232;
}

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 2020045 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))