Average Error: 33.9 → 0.5
Time: 10.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|
double f(double x, double y, double z, double t) {
        double r693821 = x;
        double r693822 = r693821 * r693821;
        double r693823 = y;
        double r693824 = r693823 * r693823;
        double r693825 = r693822 / r693824;
        double r693826 = z;
        double r693827 = r693826 * r693826;
        double r693828 = t;
        double r693829 = r693828 * r693828;
        double r693830 = r693827 / r693829;
        double r693831 = r693825 + r693830;
        return r693831;
}
↓
double f(double x, double y, double z, double t) {
        double r693832 = x;
        double r693833 = y;
        double r693834 = r693832 / r693833;
        double r693835 = fabs(r693834);
        double r693836 = sqrt(r693835);
        double r693837 = 1.5;
        double r693838 = pow(r693835, r693837);
        double r693839 = r693836 * r693838;
        double r693840 = z;
        double r693841 = t;
        double r693842 = r693840 / r693841;
        double r693843 = fabs(r693842);
        double r693844 = r693843 * r693843;
        double r693845 = r693839 + r693844;
        return r693845;
}

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

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

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

  4. Simplified34.0

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

  5. Simplified19.5

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

  7. Applied add-sqr-sqrt19.5

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

  8. Simplified19.5

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

  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 pow1/20.6

    \[\leadsto \sqrt{\left|\frac{x}{y}\right|} \cdot {\color{blue}{\left({\left(\left|\frac{x}{y}\right|\right)}^{\frac{1}{2}}\right)}}^{3} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]

  16. Applied pow-pow0.5

    \[\leadsto \sqrt{\left|\frac{x}{y}\right|} \cdot \color{blue}{{\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{1}{2} \cdot 3\right)}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]

  17. Simplified0.5

    \[\leadsto \sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\color{blue}{\frac{3}{2}}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]

  18. Final simplification0.5

    \[\leadsto \sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]

Reproduce

herbie shell --seed 2020042 
(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))))