Average Error: 34.3 → 0.5
Time: 4.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}\]
\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(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}
double f(double x, double y, double z, double t) {
        double r650121 = x;
        double r650122 = r650121 * r650121;
        double r650123 = y;
        double r650124 = r650123 * r650123;
        double r650125 = r650122 / r650124;
        double r650126 = z;
        double r650127 = r650126 * r650126;
        double r650128 = t;
        double r650129 = r650128 * r650128;
        double r650130 = r650127 / r650129;
        double r650131 = r650125 + r650130;
        return r650131;
}
↓
double f(double x, double y, double z, double t) {
        double r650132 = x;
        double r650133 = y;
        double r650134 = r650132 / r650133;
        double r650135 = fabs(r650134);
        double r650136 = r650135 * r650135;
        double r650137 = z;
        double r650138 = t;
        double r650139 = r650137 / r650138;
        double r650140 = fabs(r650139);
        double r650141 = sqrt(r650140);
        double r650142 = 1.5;
        double r650143 = pow(r650140, r650142);
        double r650144 = r650141 * r650143;
        double r650145 = r650136 + r650144;
        return r650145;
}

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

Original34.3
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.3

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

  3. Applied add-sqr-sqrt34.4

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

  4. Simplified34.3

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

  5. Simplified19.5

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

  7. Applied add-sqr-sqrt19.5

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

  8. Simplified19.5

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

  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

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

  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. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2020036 
(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))))