Average Error: 33.6 → 0.5
Time: 13.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}
double f(double x, double y, double z, double t) {
        double r424521 = x;
        double r424522 = r424521 * r424521;
        double r424523 = y;
        double r424524 = r424523 * r424523;
        double r424525 = r424522 / r424524;
        double r424526 = z;
        double r424527 = r424526 * r424526;
        double r424528 = t;
        double r424529 = r424528 * r424528;
        double r424530 = r424527 / r424529;
        double r424531 = r424525 + r424530;
        return r424531;
}
↓
double f(double x, double y, double z, double t) {
        double r424532 = x;
        double r424533 = y;
        double r424534 = r424532 / r424533;
        double r424535 = r424534 * r424534;
        double r424536 = z;
        double r424537 = t;
        double r424538 = r424536 / r424537;
        double r424539 = fabs(r424538);
        double r424540 = sqrt(r424539);
        double r424541 = 1.5;
        double r424542 = pow(r424539, r424541);
        double r424543 = r424540 * r424542;
        double r424544 = r424535 + r424543;
        return r424544;
}

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

Original33.6
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.6

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

  3. Applied times-frac18.7

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

  5. Applied add-sqr-sqrt18.8

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

  6. Simplified18.7

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

  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 pow1/20.6

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

  14. Applied pow-pow0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(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))))