Average Error: 33.9 → 0.6
Time: 8.2s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}
double f(double x, double y, double z, double t) {
        double r701665 = x;
        double r701666 = r701665 * r701665;
        double r701667 = y;
        double r701668 = r701667 * r701667;
        double r701669 = r701666 / r701668;
        double r701670 = z;
        double r701671 = r701670 * r701670;
        double r701672 = t;
        double r701673 = r701672 * r701672;
        double r701674 = r701671 / r701673;
        double r701675 = r701669 + r701674;
        return r701675;
}
↓
double f(double x, double y, double z, double t) {
        double r701676 = x;
        double r701677 = y;
        double r701678 = r701676 / r701677;
        double r701679 = fabs(r701678);
        double r701680 = r701679 * r701679;
        double r701681 = z;
        double r701682 = t;
        double r701683 = r701681 / r701682;
        double r701684 = fabs(r701683);
        double r701685 = sqrt(r701684);
        double r701686 = 3.0;
        double r701687 = pow(r701685, r701686);
        double r701688 = r701685 * r701687;
        double r701689 = r701680 + r701688;
        return r701689;
}

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

Original33.9
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

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

  3. Applied add-sqr-sqrt34.0

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

  4. Simplified33.9

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

  5. Simplified19.4

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

  7. Applied add-sqr-sqrt19.4

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

  8. Simplified19.4

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.6

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

  14. Final simplification0.6

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

Reproduce

herbie shell --seed 2020047 
(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))))