Average Error: 34.2 → 0.7
Time: 12.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \left(\sqrt{\sqrt{\left|\frac{x}{y}\right|}} \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}}\right) + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \left(\sqrt{\sqrt{\left|\frac{x}{y}\right|}} \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}}\right) + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r448628 = x;
        double r448629 = r448628 * r448628;
        double r448630 = y;
        double r448631 = r448630 * r448630;
        double r448632 = r448629 / r448631;
        double r448633 = z;
        double r448634 = r448633 * r448633;
        double r448635 = t;
        double r448636 = r448635 * r448635;
        double r448637 = r448634 / r448636;
        double r448638 = r448632 + r448637;
        return r448638;
}
↓
double f(double x, double y, double z, double t) {
        double r448639 = x;
        double r448640 = y;
        double r448641 = r448639 / r448640;
        double r448642 = fabs(r448641);
        double r448643 = sqrt(r448642);
        double r448644 = 3.0;
        double r448645 = pow(r448643, r448644);
        double r448646 = sqrt(r448643);
        double r448647 = r448646 * r448646;
        double r448648 = r448645 * r448647;
        double r448649 = z;
        double r448650 = t;
        double r448651 = r448649 / r448650;
        double r448652 = r448651 * r448651;
        double r448653 = r448648 + r448652;
        return r448653;
}

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

Original34.2
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.2

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

  3. Applied times-frac19.4

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

  5. Applied add-sqr-sqrt19.5

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

  6. Simplified19.4

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

  7. Simplified0.4

    \[\leadsto \left|\frac{x}{y}\right| \cdot \color{blue}{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
  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-sqr-sqrt0.6

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

  14. Applied sqrt-prod0.7

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

  15. Final simplification0.7

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

Reproduce

herbie shell --seed 2019303 
(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))))