Average Error: 33.9 → 0.7
Time: 22.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\frac{x}{y} \cdot \left(\sqrt[3]{\frac{1}{y}} \cdot \sqrt[3]{x}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\frac{x}{y} \cdot \left(\sqrt[3]{\frac{1}{y}} \cdot \sqrt[3]{x}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r29192119 = x;
        double r29192120 = r29192119 * r29192119;
        double r29192121 = y;
        double r29192122 = r29192121 * r29192121;
        double r29192123 = r29192120 / r29192122;
        double r29192124 = z;
        double r29192125 = r29192124 * r29192124;
        double r29192126 = t;
        double r29192127 = r29192126 * r29192126;
        double r29192128 = r29192125 / r29192127;
        double r29192129 = r29192123 + r29192128;
        return r29192129;
}
↓
double f(double x, double y, double z, double t) {
        double r29192130 = x;
        double r29192131 = y;
        double r29192132 = r29192130 / r29192131;
        double r29192133 = r29192132 * r29192132;
        double r29192134 = cbrt(r29192133);
        double r29192135 = 1.0;
        double r29192136 = r29192135 / r29192131;
        double r29192137 = cbrt(r29192136);
        double r29192138 = cbrt(r29192130);
        double r29192139 = r29192137 * r29192138;
        double r29192140 = r29192132 * r29192139;
        double r29192141 = r29192134 * r29192140;
        double r29192142 = z;
        double r29192143 = t;
        double r29192144 = r29192142 / r29192143;
        double r29192145 = r29192144 * r29192144;
        double r29192146 = r29192141 + r29192145;
        return r29192146;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Simplified0.4

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

  4. Applied add-cube-cbrt0.8

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

  5. Applied associate-*l*0.8

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

  7. Applied cbrt-unprod0.6

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

  9. Applied div-inv0.6

    \[\leadsto \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\sqrt[3]{\color{blue}{x \cdot \frac{1}{y}}} \cdot \frac{x}{y}\right) + \frac{z}{t} \cdot \frac{z}{t}\]

  10. Applied cbrt-prod0.7

    \[\leadsto \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{\frac{1}{y}}\right)} \cdot \frac{x}{y}\right) + \frac{z}{t} \cdot \frac{z}{t}\]

  11. Final simplification0.7

    \[\leadsto \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\frac{x}{y} \cdot \left(\sqrt[3]{\frac{1}{y}} \cdot \sqrt[3]{x}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}\]

Reproduce

herbie shell --seed 2019174 
(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))))