Average Error: 33.9 → 0.7
Time: 30.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{\frac{x}{y}}{\frac{y}{x}} + \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{\frac{x}{y}}{\frac{y}{x}} + \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right)
double f(double x, double y, double z, double t) {
        double r516713 = x;
        double r516714 = r516713 * r516713;
        double r516715 = y;
        double r516716 = r516715 * r516715;
        double r516717 = r516714 / r516716;
        double r516718 = z;
        double r516719 = r516718 * r516718;
        double r516720 = t;
        double r516721 = r516720 * r516720;
        double r516722 = r516719 / r516721;
        double r516723 = r516717 + r516722;
        return r516723;
}
↓
double f(double x, double y, double z, double t) {
        double r516724 = x;
        double r516725 = y;
        double r516726 = r516724 / r516725;
        double r516727 = r516725 / r516724;
        double r516728 = r516726 / r516727;
        double r516729 = z;
        double r516730 = t;
        double r516731 = r516729 / r516730;
        double r516732 = r516731 * r516731;
        double r516733 = cbrt(r516732);
        double r516734 = r516733 * r516733;
        double r516735 = r516733 * r516734;
        double r516736 = r516728 + r516735;
        return r516736;
}

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

Original33.9
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

  2. Simplified13.1

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

  4. Applied *-un-lft-identity13.1

    \[\leadsto \frac{x}{\frac{y \cdot y}{\color{blue}{1 \cdot x}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  5. Applied times-frac4.0

    \[\leadsto \frac{x}{\color{blue}{\frac{y}{1} \cdot \frac{y}{x}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  6. Applied associate-/r*0.4

    \[\leadsto \color{blue}{\frac{\frac{x}{\frac{y}{1}}}{\frac{y}{x}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  7. Simplified0.4

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

  9. Applied add-cube-cbrt0.7

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

  10. Final simplification0.7

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))