Average Error: 33.8 → 0.8
Time: 4.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|} \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}\right) \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|} \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}\right) \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}
double f(double x, double y, double z, double t) {
        double r622661 = x;
        double r622662 = r622661 * r622661;
        double r622663 = y;
        double r622664 = r622663 * r622663;
        double r622665 = r622662 / r622664;
        double r622666 = z;
        double r622667 = r622666 * r622666;
        double r622668 = t;
        double r622669 = r622668 * r622668;
        double r622670 = r622667 / r622669;
        double r622671 = r622665 + r622670;
        return r622671;
}
↓
double f(double x, double y, double z, double t) {
        double r622672 = x;
        double r622673 = y;
        double r622674 = r622672 / r622673;
        double r622675 = r622674 * r622674;
        double r622676 = z;
        double r622677 = t;
        double r622678 = r622676 / r622677;
        double r622679 = fabs(r622678);
        double r622680 = r622679 * r622679;
        double r622681 = cbrt(r622680);
        double r622682 = r622681 * r622681;
        double r622683 = r622682 * r622681;
        double r622684 = r622675 + r622683;
        return r622684;
}

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

Derivation

  1. Initial program 33.8

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt33.8

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

  4. Simplified33.8

    \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\left|\frac{z}{t}\right|} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}\]

  5. Simplified19.0

    \[\leadsto \frac{x \cdot x}{y \cdot y} + \left|\frac{z}{t}\right| \cdot \color{blue}{\left|\frac{z}{t}\right|}\]
  6. Using strategy rm

  7. Applied times-frac0.4

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.8

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

  10. Final simplification0.8

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|} \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}\right) \cdot \sqrt[3]{\left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|}\]

Reproduce

herbie shell --seed 2020056 
(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))))