Average Error: 31.3 → 0.0
Time: 10.3s
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 r554656 = x;
        double r554657 = r554656 * r554656;
        double r554658 = y;
        double r554659 = r554658 * r554658;
        double r554660 = r554657 + r554659;
        double r554661 = sqrt(r554660);
        return r554661;
}
↓
double f(double x, double y) {
        double r554662 = x;
        double r554663 = y;
        double r554664 = hypot(r554662, r554663);
        return r554664;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.3
Target17.7
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 31.3

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

  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 2019326 +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))))