Average Error: 33.9 → 0.7
Time: 39.3s
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 r540053 = x;
        double r540054 = r540053 * r540053;
        double r540055 = y;
        double r540056 = r540055 * r540055;
        double r540057 = r540054 / r540056;
        double r540058 = z;
        double r540059 = r540058 * r540058;
        double r540060 = t;
        double r540061 = r540060 * r540060;
        double r540062 = r540059 / r540061;
        double r540063 = r540057 + r540062;
        return r540063;
}
↓
double f(double x, double y, double z, double t) {
        double r540064 = x;
        double r540065 = y;
        double r540066 = r540064 / r540065;
        double r540067 = r540065 / r540064;
        double r540068 = r540066 / r540067;
        double r540069 = z;
        double r540070 = t;
        double r540071 = r540069 / r540070;
        double r540072 = r540071 * r540071;
        double r540073 = cbrt(r540072);
        double r540074 = r540073 * r540073;
        double r540075 = r540073 * r540074;
        double r540076 = r540068 + r540075;
        return r540076;
}

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))))