Average Error: 33.8 → 0.7
Time: 6.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\left|\sqrt[3]{\left|\frac{x}{y}\right|}\right| \cdot \sqrt{\sqrt[3]{\left|\frac{x}{y}\right|}}\right) \cdot {\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\left|\sqrt[3]{\left|\frac{x}{y}\right|}\right| \cdot \sqrt{\sqrt[3]{\left|\frac{x}{y}\right|}}\right) \cdot {\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 r641455 = x;
        double r641456 = r641455 * r641455;
        double r641457 = y;
        double r641458 = r641457 * r641457;
        double r641459 = r641456 / r641458;
        double r641460 = z;
        double r641461 = r641460 * r641460;
        double r641462 = t;
        double r641463 = r641462 * r641462;
        double r641464 = r641461 / r641463;
        double r641465 = r641459 + r641464;
        return r641465;
}
↓
double f(double x, double y, double z, double t) {
        double r641466 = x;
        double r641467 = y;
        double r641468 = r641466 / r641467;
        double r641469 = fabs(r641468);
        double r641470 = cbrt(r641469);
        double r641471 = fabs(r641470);
        double r641472 = sqrt(r641470);
        double r641473 = r641471 * r641472;
        double r641474 = sqrt(r641469);
        double r641475 = 3.0;
        double r641476 = pow(r641474, r641475);
        double r641477 = r641473 * r641476;
        double r641478 = z;
        double r641479 = t;
        double r641480 = r641478 / r641479;
        double r641481 = r641480 * r641480;
        double r641482 = r641477 + r641481;
        return r641482;
}

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

Original33.8
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
  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-sqrt19.4

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

  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

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied add-cube-cbrt0.7

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

  14. Applied sqrt-prod0.7

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

  15. Simplified0.7

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

  16. Final simplification0.7

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

Reproduce

herbie shell --seed 2020045 
(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))))