Average Error: 33.7 → 0.6
Time: 4.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt{\sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}} \cdot \sqrt{\sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}}\right) \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt{\sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}} \cdot \sqrt{\sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}}\right) \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r677261 = x;
        double r677262 = r677261 * r677261;
        double r677263 = y;
        double r677264 = r677263 * r677263;
        double r677265 = r677262 / r677264;
        double r677266 = z;
        double r677267 = r677266 * r677266;
        double r677268 = t;
        double r677269 = r677268 * r677268;
        double r677270 = r677267 / r677269;
        double r677271 = r677265 + r677270;
        return r677271;
}
↓
double f(double x, double y, double z, double t) {
        double r677272 = x;
        double r677273 = y;
        double r677274 = r677272 / r677273;
        double r677275 = r677274 * r677274;
        double r677276 = z;
        double r677277 = t;
        double r677278 = r677276 / r677277;
        double r677279 = r677278 * r677278;
        double r677280 = r677275 + r677279;
        double r677281 = sqrt(r677280);
        double r677282 = sqrt(r677281);
        double r677283 = r677282 * r677282;
        double r677284 = r677283 * r677281;
        return r677284;
}

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

Original33.7
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.7

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

  3. Applied times-frac19.4

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

  5. Applied times-frac0.4

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

  7. Applied add-sqr-sqrt0.4

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

  9. Applied add-sqr-sqrt0.4

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

  10. Applied sqrt-prod0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2020064 
(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))))