Average Error: 33.6 → 0.5
Time: 18.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|
double f(double x, double y, double z, double t) {
        double r375109 = x;
        double r375110 = r375109 * r375109;
        double r375111 = y;
        double r375112 = r375111 * r375111;
        double r375113 = r375110 / r375112;
        double r375114 = z;
        double r375115 = r375114 * r375114;
        double r375116 = t;
        double r375117 = r375116 * r375116;
        double r375118 = r375115 / r375117;
        double r375119 = r375113 + r375118;
        return r375119;
}
↓
double f(double x, double y, double z, double t) {
        double r375120 = x;
        double r375121 = y;
        double r375122 = r375120 / r375121;
        double r375123 = fabs(r375122);
        double r375124 = sqrt(r375123);
        double r375125 = 1.5;
        double r375126 = pow(r375123, r375125);
        double r375127 = r375124 * r375126;
        double r375128 = z;
        double r375129 = t;
        double r375130 = r375128 / r375129;
        double r375131 = fabs(r375130);
        double r375132 = r375131 * r375131;
        double r375133 = r375127 + r375132;
        return r375133;
}

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 add-sqr-sqrt33.7

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

  4. Simplified33.7

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

  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

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.6

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

  15. Applied pow1/20.6

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

  16. Applied pow-pow0.5

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

  17. Simplified0.5

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

  18. Final simplification0.5

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

Reproduce

herbie shell --seed 2019322 
(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))))