Average Error: 33.9 → 0.7
Time: 22.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \sqrt[3]{\frac{x}{y}} \cdot \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{\frac{x}{y}}}{\sqrt[3]{y}} \cdot \frac{x}{y}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \sqrt[3]{\frac{x}{y}} \cdot \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{\frac{x}{y}}}{\sqrt[3]{y}} \cdot \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r44655563 = x;
        double r44655564 = r44655563 * r44655563;
        double r44655565 = y;
        double r44655566 = r44655565 * r44655565;
        double r44655567 = r44655564 / r44655566;
        double r44655568 = z;
        double r44655569 = r44655568 * r44655568;
        double r44655570 = t;
        double r44655571 = r44655570 * r44655570;
        double r44655572 = r44655569 / r44655571;
        double r44655573 = r44655567 + r44655572;
        return r44655573;
}
↓
double f(double x, double y, double z, double t) {
        double r44655574 = z;
        double r44655575 = t;
        double r44655576 = r44655574 / r44655575;
        double r44655577 = r44655576 * r44655576;
        double r44655578 = x;
        double r44655579 = y;
        double r44655580 = r44655578 / r44655579;
        double r44655581 = cbrt(r44655580);
        double r44655582 = cbrt(r44655578);
        double r44655583 = r44655582 * r44655581;
        double r44655584 = cbrt(r44655579);
        double r44655585 = r44655583 / r44655584;
        double r44655586 = r44655585 * r44655580;
        double r44655587 = r44655581 * r44655586;
        double r44655588 = r44655577 + r44655587;
        return r44655588;
}

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

Original33.9
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

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

  5. Applied associate-*r*0.8

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

  7. Applied cbrt-div0.7

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

  8. Applied associate-*l/0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2019171 
(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))))