Average Error: 33.2 → 0.7
Time: 14.9s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right) \cdot \left(\sqrt[3]{{\left(\sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)}^{3}} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right) \cdot \left(\sqrt[3]{{\left(\sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)}^{3}} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)
double f(double x, double y, double z, double t) {
        double r475748 = x;
        double r475749 = r475748 * r475748;
        double r475750 = y;
        double r475751 = r475750 * r475750;
        double r475752 = r475749 / r475751;
        double r475753 = z;
        double r475754 = r475753 * r475753;
        double r475755 = t;
        double r475756 = r475755 * r475755;
        double r475757 = r475754 / r475756;
        double r475758 = r475752 + r475757;
        return r475758;
}
↓
double f(double x, double y, double z, double t) {
        double r475759 = x;
        double r475760 = y;
        double r475761 = r475759 / r475760;
        double r475762 = z;
        double r475763 = t;
        double r475764 = r475762 / r475763;
        double r475765 = hypot(r475761, r475764);
        double r475766 = sqrt(r475765);
        double r475767 = 3.0;
        double r475768 = pow(r475766, r475767);
        double r475769 = cbrt(r475768);
        double r475770 = r475769 * r475766;
        double r475771 = r475765 * r475770;
        return r475771;
}

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

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

Derivation

  1. Initial program 33.2

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

  2. Simplified18.9

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

  4. Applied add-sqr-sqrt19.0

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

  5. Simplified18.9

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

  6. Simplified0.4

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

  8. Applied add-sqr-sqrt0.6

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

  10. Applied add-cbrt-cube0.7

    \[\leadsto \mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right) \cdot \left(\color{blue}{\sqrt[3]{\left(\sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right) \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}}} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)\]

  11. Simplified0.7

    \[\leadsto \mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right) \cdot \left(\sqrt[3]{\color{blue}{{\left(\sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)}^{3}}} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)\]

  12. Final simplification0.7

    \[\leadsto \mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right) \cdot \left(\sqrt[3]{{\left(\sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)}^{3}} \cdot \sqrt{\mathsf{hypot}\left(\frac{x}{y}, \frac{z}{t}\right)}\right)\]

Reproduce

herbie shell --seed 2019212 +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))))