Average Error: 33.9 → 0.6
Time: 10.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}
double f(double x, double y, double z, double t) {
        double r752619 = x;
        double r752620 = r752619 * r752619;
        double r752621 = y;
        double r752622 = r752621 * r752621;
        double r752623 = r752620 / r752622;
        double r752624 = z;
        double r752625 = r752624 * r752624;
        double r752626 = t;
        double r752627 = r752626 * r752626;
        double r752628 = r752625 / r752627;
        double r752629 = r752623 + r752628;
        return r752629;
}
↓
double f(double x, double y, double z, double t) {
        double r752630 = x;
        double r752631 = y;
        double r752632 = r752630 / r752631;
        double r752633 = fabs(r752632);
        double r752634 = r752633 * r752633;
        double r752635 = z;
        double r752636 = t;
        double r752637 = r752635 / r752636;
        double r752638 = fabs(r752637);
        double r752639 = sqrt(r752638);
        double r752640 = 3.0;
        double r752641 = pow(r752639, r752640);
        double r752642 = r752639 * r752641;
        double r752643 = r752634 + r752642;
        return r752643;
}

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

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

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

  4. Simplified33.9

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

  5. Simplified19.4

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

  7. Applied add-sqr-sqrt19.4

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

  8. Simplified19.4

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.6

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

  14. Final simplification0.6

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

Reproduce

herbie shell --seed 2020047 
(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))))