Average Error: 32.3 → 0.6
Time: 16.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\frac{1}{t}}\right)\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\frac{1}{t}}\right)\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r28734525 = x;
        double r28734526 = r28734525 * r28734525;
        double r28734527 = y;
        double r28734528 = r28734527 * r28734527;
        double r28734529 = r28734526 / r28734528;
        double r28734530 = z;
        double r28734531 = r28734530 * r28734530;
        double r28734532 = t;
        double r28734533 = r28734532 * r28734532;
        double r28734534 = r28734531 / r28734533;
        double r28734535 = r28734529 + r28734534;
        return r28734535;
}
↓
double f(double x, double y, double z, double t) {
        double r28734536 = z;
        double r28734537 = t;
        double r28734538 = r28734536 / r28734537;
        double r28734539 = cbrt(r28734538);
        double r28734540 = cbrt(r28734536);
        double r28734541 = 1.0;
        double r28734542 = r28734541 / r28734537;
        double r28734543 = cbrt(r28734542);
        double r28734544 = r28734540 * r28734543;
        double r28734545 = r28734539 * r28734544;
        double r28734546 = r28734539 * r28734538;
        double r28734547 = r28734545 * r28734546;
        double r28734548 = x;
        double r28734549 = y;
        double r28734550 = r28734548 / r28734549;
        double r28734551 = r28734550 * r28734550;
        double r28734552 = r28734547 + r28734551;
        double r28734553 = sqrt(r28734552);
        double r28734554 = r28734538 * r28734538;
        double r28734555 = r28734551 + r28734554;
        double r28734556 = sqrt(r28734555);
        double r28734557 = r28734553 * r28734556;
        return r28734557;
}

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

Original32.3
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 32.3

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

  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-sqr-sqrt0.4

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied associate-*l*0.6

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

  9. Applied div-inv0.6

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

  10. Applied cbrt-prod0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

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