Average Error: 33.5 → 0.6
Time: 4.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}}
double f(double x, double y, double z, double t) {
        double r878229 = x;
        double r878230 = r878229 * r878229;
        double r878231 = y;
        double r878232 = r878231 * r878231;
        double r878233 = r878230 / r878232;
        double r878234 = z;
        double r878235 = r878234 * r878234;
        double r878236 = t;
        double r878237 = r878236 * r878236;
        double r878238 = r878235 / r878237;
        double r878239 = r878233 + r878238;
        return r878239;
}
↓
double f(double x, double y, double z, double t) {
        double r878240 = x;
        double r878241 = y;
        double r878242 = r878240 / r878241;
        double r878243 = fabs(r878242);
        double r878244 = r878243 * r878243;
        double r878245 = z;
        double r878246 = t;
        double r878247 = r878245 / r878246;
        double r878248 = r878247 * r878247;
        double r878249 = r878244 + r878248;
        double r878250 = sqrt(r878249);
        double r878251 = cbrt(r878248);
        double r878252 = r878251 * r878251;
        double r878253 = r878252 * r878251;
        double r878254 = r878244 + r878253;
        double r878255 = sqrt(r878254);
        double r878256 = r878250 * r878255;
        return r878256;
}

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

Original33.5
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.5

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

  3. Applied times-frac18.5

    \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt18.5

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

  6. Simplified18.5

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

  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-sqrt0.4

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

  11. Applied add-cube-cbrt0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2019353 
(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))))