Average Error: 32.2 → 0.7
Time: 17.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right) \cdot \frac{z}{t}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right) \cdot \frac{z}{t}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r31526596 = x;
        double r31526597 = r31526596 * r31526596;
        double r31526598 = y;
        double r31526599 = r31526598 * r31526598;
        double r31526600 = r31526597 / r31526599;
        double r31526601 = z;
        double r31526602 = r31526601 * r31526601;
        double r31526603 = t;
        double r31526604 = r31526603 * r31526603;
        double r31526605 = r31526602 / r31526604;
        double r31526606 = r31526600 + r31526605;
        return r31526606;
}
↓
double f(double x, double y, double z, double t) {
        double r31526607 = 1.0;
        double r31526608 = t;
        double r31526609 = r31526607 / r31526608;
        double r31526610 = cbrt(r31526609);
        double r31526611 = z;
        double r31526612 = cbrt(r31526611);
        double r31526613 = r31526610 * r31526612;
        double r31526614 = r31526611 / r31526608;
        double r31526615 = r31526613 * r31526614;
        double r31526616 = cbrt(r31526614);
        double r31526617 = r31526616 * r31526616;
        double r31526618 = r31526615 * r31526617;
        double r31526619 = x;
        double r31526620 = y;
        double r31526621 = r31526619 / r31526620;
        double r31526622 = r31526621 * r31526621;
        double r31526623 = r31526618 + r31526622;
        return r31526623;
}

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

Original32.2
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 32.2

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

  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

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

  5. Applied associate-*l*0.8

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

  6. Taylor expanded around 0 46.7

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

  7. Simplified0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019163 
(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))))