Average Error: 29.6 → 0.0
Time: 1.3s
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 r40229110 = x;
        double r40229111 = r40229110 * r40229110;
        double r40229112 = y;
        double r40229113 = r40229112 * r40229112;
        double r40229114 = r40229111 + r40229113;
        double r40229115 = sqrt(r40229114);
        return r40229115;
}
↓
double f(double x, double y) {
        double r40229116 = x;
        double r40229117 = y;
        double r40229118 = hypot(r40229116, r40229117);
        return r40229118;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.6
Target17.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Initial program 29.6

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

  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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

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