Average Error: 33.4 → 0.5
Time: 4.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt{{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}}}\right) \cdot \sqrt{\left|\frac{x}{y}\right|} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt{{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}}}\right) \cdot \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 r690125 = x;
        double r690126 = r690125 * r690125;
        double r690127 = y;
        double r690128 = r690127 * r690127;
        double r690129 = r690126 / r690128;
        double r690130 = z;
        double r690131 = r690130 * r690130;
        double r690132 = t;
        double r690133 = r690132 * r690132;
        double r690134 = r690131 / r690133;
        double r690135 = r690129 + r690134;
        return r690135;
}
↓
double f(double x, double y, double z, double t) {
        double r690136 = x;
        double r690137 = y;
        double r690138 = r690136 / r690137;
        double r690139 = fabs(r690138);
        double r690140 = 1.5;
        double r690141 = pow(r690139, r690140);
        double r690142 = sqrt(r690141);
        double r690143 = r690142 * r690142;
        double r690144 = sqrt(r690139);
        double r690145 = r690143 * r690144;
        double r690146 = z;
        double r690147 = t;
        double r690148 = r690146 / r690147;
        double r690149 = fabs(r690148);
        double r690150 = r690149 * r690149;
        double r690151 = r690145 + r690150;
        return r690151;
}

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

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

Derivation

  1. Initial program 33.4

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

  3. Applied add-sqr-sqrt33.5

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

  4. Simplified33.4

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

  5. Simplified19.3

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

  7. Applied add-sqr-sqrt19.3

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

  8. Simplified19.3

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

  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

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2020065 
(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))))