Average Error: 33.5 → 0.7
Time: 16.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\left|\frac{x}{y}\right|} \cdot \sqrt[3]{\sqrt{\left|\frac{x}{y}\right|}}\right) \cdot {\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt[3]{\left|\frac{x}{y}\right|} \cdot \sqrt[3]{\sqrt{\left|\frac{x}{y}\right|}}\right) \cdot {\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|
double f(double x, double y, double z, double t) {
        double r452703 = x;
        double r452704 = r452703 * r452703;
        double r452705 = y;
        double r452706 = r452705 * r452705;
        double r452707 = r452704 / r452706;
        double r452708 = z;
        double r452709 = r452708 * r452708;
        double r452710 = t;
        double r452711 = r452710 * r452710;
        double r452712 = r452709 / r452711;
        double r452713 = r452707 + r452712;
        return r452713;
}
↓
double f(double x, double y, double z, double t) {
        double r452714 = x;
        double r452715 = y;
        double r452716 = r452714 / r452715;
        double r452717 = fabs(r452716);
        double r452718 = cbrt(r452717);
        double r452719 = sqrt(r452717);
        double r452720 = cbrt(r452719);
        double r452721 = r452718 * r452720;
        double r452722 = 3.0;
        double r452723 = pow(r452719, r452722);
        double r452724 = r452721 * r452723;
        double r452725 = z;
        double r452726 = t;
        double r452727 = r452725 / r452726;
        double r452728 = fabs(r452727);
        double r452729 = r452728 * r452728;
        double r452730 = r452724 + r452729;
        return r452730;
}

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

Original33.5
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.5

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

  3. Applied add-sqr-sqrt33.5

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

  4. Simplified33.5

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

  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 add-sqr-sqrt19.0

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

  8. Simplified19.0

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.6

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

  15. Applied add-cube-cbrt0.8

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

  16. Simplified0.7

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

  17. Final simplification0.7

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

Reproduce

herbie shell --seed 2019306 
(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))))