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 r736267 = x;
        double r736268 = r736267 * r736267;
        double r736269 = y;
        double r736270 = r736269 * r736269;
        double r736271 = r736268 + r736270;
        double r736272 = sqrt(r736271);
        return r736272;
}
↓
double f(double x, double y) {
        double r736273 = x;
        double r736274 = y;
        double r736275 = hypot(r736273, r736274);
        return r736275;
}

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))))