Average Error: 0.1 → 0.1
Time: 15.9s
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 r7692395 = 1.0;
        double r7692396 = 2.0;
        double r7692397 = r7692395 / r7692396;
        double r7692398 = x;
        double r7692399 = y;
        double r7692400 = z;
        double r7692401 = sqrt(r7692400);
        double r7692402 = r7692399 * r7692401;
        double r7692403 = r7692398 + r7692402;
        double r7692404 = r7692397 * r7692403;
        return r7692404;
}
↓
double f(double x, double y, double z) {
        double r7692405 = 1.0;
        double r7692406 = 2.0;
        double r7692407 = r7692405 / r7692406;
        double r7692408 = x;
        double r7692409 = z;
        double r7692410 = sqrt(r7692409);
        double r7692411 = y;
        double r7692412 = r7692410 * r7692411;
        double r7692413 = r7692408 + r7692412;
        double r7692414 = r7692407 * r7692413;
        return r7692414;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))