Average Error: 33.4 → 0.7
Time: 4.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \sqrt[3]{{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \sqrt[3]{{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3}} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r608589 = x;
        double r608590 = r608589 * r608589;
        double r608591 = y;
        double r608592 = r608591 * r608591;
        double r608593 = r608590 / r608592;
        double r608594 = z;
        double r608595 = r608594 * r608594;
        double r608596 = t;
        double r608597 = r608596 * r608596;
        double r608598 = r608595 / r608597;
        double r608599 = r608593 + r608598;
        return r608599;
}
↓
double f(double x, double y, double z, double t) {
        double r608600 = x;
        double r608601 = y;
        double r608602 = r608600 / r608601;
        double r608603 = fabs(r608602);
        double r608604 = sqrt(r608603);
        double r608605 = 3.0;
        double r608606 = pow(r608604, r608605);
        double r608607 = cbrt(r608606);
        double r608608 = r608606 * r608607;
        double r608609 = z;
        double r608610 = t;
        double r608611 = r608609 / r608610;
        double r608612 = r608611 * r608611;
        double r608613 = r608608 + r608612;
        return r608613;
}

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

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

Derivation

  1. Initial program 33.4

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

  3. Applied add-sqr-sqrt33.5

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

  4. Simplified33.4

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

  5. Simplified18.7

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

  7. Applied times-frac0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

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

  13. Applied add-cbrt-cube0.7

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

  14. Simplified0.7

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

  15. Final simplification0.7

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

Reproduce

herbie shell --seed 2019356 
(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))))