Average Error: 31.0 → 0.0
Time: 1.5s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\mathsf{hypot}\left(x, y\right)\]
\sqrt{x \cdot x + y \cdot y}
↓
\mathsf{hypot}\left(x, y\right)
double f(double x, double y) {
        double r743868 = x;
        double r743869 = r743868 * r743868;
        double r743870 = y;
        double r743871 = r743870 * r743870;
        double r743872 = r743869 + r743871;
        double r743873 = sqrt(r743872);
        return r743873;
}
↓
double f(double x, double y) {
        double r743874 = x;
        double r743875 = y;
        double r743876 = hypot(r743874, r743875);
        return r743876;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.0
Target17.2
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659982632437974301616192301785 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362039388201959321597704512 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Initial program 31.0

    \[\sqrt{x \cdot x + y \cdot y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{hypot}\left(x, y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{hypot}\left(x, y\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.123695082659983e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

  (sqrt (+ (* x x) (* y y))))