Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{\left(\sqrt{z} \cdot y + x\right) \cdot 1}{2}\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{\left(\sqrt{z} \cdot y + x\right) \cdot 1}{2}
double code(double x, double y, double z) {
	return ((1.0 / 2.0) * (x + (y * sqrt(z))));
}
↓
double code(double x, double y, double z) {
	return ((((sqrt(z) * y) + x) * 1.0) / 2.0);
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\sqrt{z}, y, x\right) \cdot 1}{2}}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020066 +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)))))