Average Error: 35.5 → 0.0
Time: 5.2s
Precision: 64
\[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]
↓
\[\mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)\]
\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}
↓
\mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)
double f(double x, double y, double z) {
        double r11294426 = x;
        double r11294427 = r11294426 * r11294426;
        double r11294428 = y;
        double r11294429 = r11294428 * r11294428;
        double r11294430 = r11294427 + r11294429;
        double r11294431 = z;
        double r11294432 = r11294431 * r11294431;
        double r11294433 = r11294430 + r11294432;
        double r11294434 = sqrt(r11294433);
        return r11294434;
}
↓
double f(double x, double y, double z) {
        double r11294435 = x;
        double r11294436 = y;
        double r11294437 = hypot(r11294435, r11294436);
        double r11294438 = z;
        double r11294439 = hypot(r11294437, r11294438);
        return r11294439;
}

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

Target

Original35.5
Target24.1
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;z \lt -6.396479394109776 \cdot 10^{+136}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \lt 7.320293694404182 \cdot 10^{+117}:\\ \;\;\;\;\sqrt{\left(z \cdot z + x \cdot x\right) + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

Derivation

  1. Initial program 35.5

    \[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt35.5

    \[\leadsto \sqrt{\color{blue}{\sqrt{x \cdot x + y \cdot y} \cdot \sqrt{x \cdot x + y \cdot y}} + z \cdot z}\]

  4. Applied hypot-def26.3

    \[\leadsto \color{blue}{\mathsf{hypot}\left(\sqrt{x \cdot x + y \cdot y}, z\right)}\]
  5. Using strategy rm

  6. Applied hypot-def0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2"

  :herbie-target
  (if (< z -6.396479394109776e+136) (- z) (if (< z 7.320293694404182e+117) (sqrt (+ (+ (* z z) (* x x)) (* y y))) z))

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