Average Error: 33.4 → 0.6
Time: 21.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\frac{z}{t} \cdot \sqrt[3]{\frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} + \frac{\frac{x}{y}}{\frac{y}{x}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\frac{z}{t} \cdot \sqrt[3]{\frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} + \frac{\frac{x}{y}}{\frac{y}{x}}
double f(double x, double y, double z, double t) {
        double r404454 = x;
        double r404455 = r404454 * r404454;
        double r404456 = y;
        double r404457 = r404456 * r404456;
        double r404458 = r404455 / r404457;
        double r404459 = z;
        double r404460 = r404459 * r404459;
        double r404461 = t;
        double r404462 = r404461 * r404461;
        double r404463 = r404460 / r404462;
        double r404464 = r404458 + r404463;
        return r404464;
}
↓
double f(double x, double y, double z, double t) {
        double r404465 = z;
        double r404466 = t;
        double r404467 = r404465 / r404466;
        double r404468 = cbrt(r404467);
        double r404469 = r404467 * r404468;
        double r404470 = r404467 * r404467;
        double r404471 = cbrt(r404470);
        double r404472 = r404469 * r404471;
        double r404473 = x;
        double r404474 = y;
        double r404475 = r404473 / r404474;
        double r404476 = r404474 / r404473;
        double r404477 = r404475 / r404476;
        double r404478 = r404472 + r404477;
        return r404478;
}

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

Original33.4
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.4

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

  2. Simplified13.3

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

  4. Applied *-un-lft-identity13.3

    \[\leadsto \frac{x}{\frac{y \cdot y}{\color{blue}{1 \cdot x}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  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

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

  10. Applied associate-*l*0.7

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

  11. Simplified0.7

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

  13. Applied cbrt-unprod0.6

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

  14. Final simplification0.6

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

Reproduce

herbie shell --seed 2019179 
(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))))