Average Error: 33.1 → 0.8
Time: 19.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \left(\frac{z}{t} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right)\right) + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \left(\frac{z}{t} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right)\right) + \frac{x}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r29540674 = x;
        double r29540675 = r29540674 * r29540674;
        double r29540676 = y;
        double r29540677 = r29540676 * r29540676;
        double r29540678 = r29540675 / r29540677;
        double r29540679 = z;
        double r29540680 = r29540679 * r29540679;
        double r29540681 = t;
        double r29540682 = r29540681 * r29540681;
        double r29540683 = r29540680 / r29540682;
        double r29540684 = r29540678 + r29540683;
        return r29540684;
}
↓
double f(double x, double y, double z, double t) {
        double r29540685 = 1.0;
        double r29540686 = t;
        double r29540687 = cbrt(r29540686);
        double r29540688 = r29540687 * r29540687;
        double r29540689 = r29540685 / r29540688;
        double r29540690 = cbrt(r29540689);
        double r29540691 = z;
        double r29540692 = r29540691 / r29540687;
        double r29540693 = cbrt(r29540692);
        double r29540694 = r29540690 * r29540693;
        double r29540695 = r29540691 / r29540686;
        double r29540696 = cbrt(r29540695);
        double r29540697 = r29540696 * r29540696;
        double r29540698 = r29540695 * r29540697;
        double r29540699 = r29540694 * r29540698;
        double r29540700 = x;
        double r29540701 = y;
        double r29540702 = r29540700 / r29540701;
        double r29540703 = r29540702 * r29540702;
        double r29540704 = r29540699 + r29540703;
        return r29540704;
}

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

Original33.1
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.1

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

  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

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

  5. Applied associate-*r*0.8

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

  7. Applied add-cube-cbrt0.8

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

  8. Applied *-un-lft-identity0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019170 
(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))))