Average Error: 0.2 → 0.2
Time: 10.0s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r155634 = 1.0;
        double r155635 = 2.0;
        double r155636 = r155634 / r155635;
        double r155637 = x;
        double r155638 = y;
        double r155639 = z;
        double r155640 = sqrt(r155639);
        double r155641 = r155638 * r155640;
        double r155642 = r155637 + r155641;
        double r155643 = r155636 * r155642;
        return r155643;
}
↓
double f(double x, double y, double z) {
        double r155644 = 1.0;
        double r155645 = 2.0;
        double r155646 = r155644 / r155645;
        double r155647 = x;
        double r155648 = z;
        double r155649 = sqrt(r155648);
        double r155650 = y;
        double r155651 = r155649 * r155650;
        double r155652 = r155647 + r155651;
        double r155653 = r155646 * r155652;
        return r155653;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +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)))))