Average Error: 33.7 → 0.4
Time: 4.8s
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 r537874 = x;
        double r537875 = r537874 * r537874;
        double r537876 = y;
        double r537877 = r537876 * r537876;
        double r537878 = r537875 / r537877;
        double r537879 = z;
        double r537880 = r537879 * r537879;
        double r537881 = t;
        double r537882 = r537881 * r537881;
        double r537883 = r537880 / r537882;
        double r537884 = r537878 + r537883;
        return r537884;
}
↓
double f(double x, double y, double z, double t) {
        double r537885 = z;
        double r537886 = t;
        double r537887 = r537885 / r537886;
        double r537888 = x;
        double r537889 = y;
        double r537890 = r537888 / r537889;
        double r537891 = hypot(r537887, r537890);
        double r537892 = r537891 * r537891;
        return r537892;
}

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

Original33.7
Target0.4
Herbie0.4
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.7

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

  2. Simplified19.3

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

  4. Applied add-sqr-sqrt19.4

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

  5. Simplified19.3

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

  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 2020001 +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))))