Average Error: 33.8 → 0.6
Time: 1.1m
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \frac{z}{t}\right) \cdot \sqrt[3]{\frac{z}{t}}\]
\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 \frac{z}{t}\right) \cdot \sqrt[3]{\frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r32857414 = x;
        double r32857415 = r32857414 * r32857414;
        double r32857416 = y;
        double r32857417 = r32857416 * r32857416;
        double r32857418 = r32857415 / r32857417;
        double r32857419 = z;
        double r32857420 = r32857419 * r32857419;
        double r32857421 = t;
        double r32857422 = r32857421 * r32857421;
        double r32857423 = r32857420 / r32857422;
        double r32857424 = r32857418 + r32857423;
        return r32857424;
}
↓
double f(double x, double y, double z, double t) {
        double r32857425 = x;
        double r32857426 = y;
        double r32857427 = r32857425 / r32857426;
        double r32857428 = r32857427 * r32857427;
        double r32857429 = z;
        double r32857430 = t;
        double r32857431 = r32857429 / r32857430;
        double r32857432 = r32857431 * r32857431;
        double r32857433 = cbrt(r32857432);
        double r32857434 = r32857433 * r32857431;
        double r32857435 = cbrt(r32857431);
        double r32857436 = r32857434 * r32857435;
        double r32857437 = r32857428 + r32857436;
        return r32857437;
}

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

Derivation

  1. Initial program 33.8

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

  2. 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 cbrt-unprod0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(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))))