Average Error: 33.8 → 0.4
Time: 3.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right) \cdot \mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right) \cdot \mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r511187 = x;
        double r511188 = r511187 * r511187;
        double r511189 = y;
        double r511190 = r511189 * r511189;
        double r511191 = r511188 / r511190;
        double r511192 = z;
        double r511193 = r511192 * r511192;
        double r511194 = t;
        double r511195 = r511194 * r511194;
        double r511196 = r511193 / r511195;
        double r511197 = r511191 + r511196;
        return r511197;
}
↓
double f(double x, double y, double z, double t) {
        double r511198 = z;
        double r511199 = t;
        double r511200 = r511198 / r511199;
        double r511201 = x;
        double r511202 = y;
        double r511203 = r511201 / r511202;
        double r511204 = hypot(r511200, r511203);
        double r511205 = r511204 * r511204;
        return r511205;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.8
Target0.4
Herbie0.4
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

  2. Simplified19.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt19.8

    \[\leadsto \color{blue}{\sqrt{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)} \cdot \sqrt{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)}}\]

  5. Simplified19.8

    \[\leadsto \color{blue}{\mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right)} \cdot \sqrt{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)}\]

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))