Average Error: 0.2 → 0.2
Time: 4.3s
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 r253495 = 1.0;
        double r253496 = 2.0;
        double r253497 = r253495 / r253496;
        double r253498 = x;
        double r253499 = y;
        double r253500 = z;
        double r253501 = sqrt(r253500);
        double r253502 = r253499 * r253501;
        double r253503 = r253498 + r253502;
        double r253504 = r253497 * r253503;
        return r253504;
}
↓
double f(double x, double y, double z) {
        double r253505 = 1.0;
        double r253506 = 2.0;
        double r253507 = r253505 / r253506;
        double r253508 = x;
        double r253509 = y;
        double r253510 = z;
        double r253511 = sqrt(r253510);
        double r253512 = r253509 * r253511;
        double r253513 = r253508 + r253512;
        double r253514 = r253507 * r253513;
        return r253514;
}

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 0.2

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.2

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))