Average Error: 33.7 → 0.7
Time: 4.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \sqrt[3]{{\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \sqrt[3]{{\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}
double f(double x, double y, double z, double t) {
        double r570658 = x;
        double r570659 = r570658 * r570658;
        double r570660 = y;
        double r570661 = r570660 * r570660;
        double r570662 = r570659 / r570661;
        double r570663 = z;
        double r570664 = r570663 * r570663;
        double r570665 = t;
        double r570666 = r570665 * r570665;
        double r570667 = r570664 / r570666;
        double r570668 = r570662 + r570667;
        return r570668;
}
↓
double f(double x, double y, double z, double t) {
        double r570669 = x;
        double r570670 = y;
        double r570671 = r570669 / r570670;
        double r570672 = r570671 * r570671;
        double r570673 = z;
        double r570674 = t;
        double r570675 = r570673 / r570674;
        double r570676 = fabs(r570675);
        double r570677 = sqrt(r570676);
        double r570678 = 3.0;
        double r570679 = pow(r570677, r570678);
        double r570680 = cbrt(r570679);
        double r570681 = r570680 * r570679;
        double r570682 = r570672 + r570681;
        return r570682;
}

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

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

Derivation

  1. Initial program 33.7

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

  3. Applied times-frac19.3

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt19.3

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

  6. Simplified19.3

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

  7. Simplified0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied add-cbrt-cube0.7

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

  14. Simplified0.7

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

  15. Final simplification0.7

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

Reproduce

herbie shell --seed 2020100 
(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))))