Average Error: 33.8 → 0.8
Time: 4.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \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 r617084 = x;
        double r617085 = r617084 * r617084;
        double r617086 = y;
        double r617087 = r617086 * r617086;
        double r617088 = r617085 / r617087;
        double r617089 = z;
        double r617090 = r617089 * r617089;
        double r617091 = t;
        double r617092 = r617091 * r617091;
        double r617093 = r617090 / r617092;
        double r617094 = r617088 + r617093;
        return r617094;
}
↓
double f(double x, double y, double z, double t) {
        double r617095 = x;
        double r617096 = y;
        double r617097 = r617095 / r617096;
        double r617098 = r617097 * r617097;
        double r617099 = z;
        double r617100 = t;
        double r617101 = r617099 / r617100;
        double r617102 = r617101 * r617101;
        double r617103 = cbrt(r617102);
        double r617104 = r617103 * r617103;
        double r617105 = r617104 * r617103;
        double r617106 = r617098 + r617105;
        return r617106;
}

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

Original33.8
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

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

  3. Applied times-frac18.8

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t}\]
  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-cube-cbrt0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2020062 
(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))))