Average Error: 0.1 → 0.1
Time: 7.3s
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 r1124 = 1.0;
        double r1125 = 2.0;
        double r1126 = r1124 / r1125;
        double r1127 = x;
        double r1128 = y;
        double r1129 = z;
        double r1130 = sqrt(r1129);
        double r1131 = r1128 * r1130;
        double r1132 = r1127 + r1131;
        double r1133 = r1126 * r1132;
        return r1133;
}
↓
double f(double x, double y, double z) {
        double r1134 = 1.0;
        double r1135 = 2.0;
        double r1136 = r1134 / r1135;
        double r1137 = x;
        double r1138 = y;
        double r1139 = z;
        double r1140 = sqrt(r1139);
        double r1141 = r1138 * r1140;
        double r1142 = r1137 + r1141;
        double r1143 = r1136 * r1142;
        return r1143;
}

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 2020025 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))