Average Error: 33.2 → 0.5
Time: 4.9s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left({\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}}\right) \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left({\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}}\right) \cdot \sqrt{\sqrt{\left|\frac{x}{y}\right|}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|
double f(double x, double y, double z, double t) {
        double r603092 = x;
        double r603093 = r603092 * r603092;
        double r603094 = y;
        double r603095 = r603094 * r603094;
        double r603096 = r603093 / r603095;
        double r603097 = z;
        double r603098 = r603097 * r603097;
        double r603099 = t;
        double r603100 = r603099 * r603099;
        double r603101 = r603098 / r603100;
        double r603102 = r603096 + r603101;
        return r603102;
}
↓
double f(double x, double y, double z, double t) {
        double r603103 = x;
        double r603104 = y;
        double r603105 = r603103 / r603104;
        double r603106 = fabs(r603105);
        double r603107 = 1.5;
        double r603108 = pow(r603106, r603107);
        double r603109 = sqrt(r603106);
        double r603110 = sqrt(r603109);
        double r603111 = r603108 * r603110;
        double r603112 = r603111 * r603110;
        double r603113 = z;
        double r603114 = t;
        double r603115 = r603113 / r603114;
        double r603116 = fabs(r603115);
        double r603117 = r603116 * r603116;
        double r603118 = r603112 + r603117;
        return r603118;
}

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

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

Derivation

  1. Initial program 33.2

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

  3. Applied add-sqr-sqrt33.2

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

  4. Simplified33.2

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

  5. Simplified18.7

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

  7. Applied add-sqr-sqrt18.8

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

  8. Simplified18.8

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Simplified0.5

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

  15. Applied add-sqr-sqrt0.5

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

  16. Applied sqrt-prod0.5

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

  17. Applied associate-*r*0.5

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

  18. Final simplification0.5

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

Reproduce

herbie shell --seed 2020034 
(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))))