Average Error: 1.4 → 0.6
Time: 1.0m
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \left(\left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\right) \cdot y\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \left(\left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\right) \cdot y\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}
double f(double x, double y, double z, double t, double a) {
        double r30718503 = x;
        double r30718504 = y;
        double r30718505 = z;
        double r30718506 = t;
        double r30718507 = r30718505 - r30718506;
        double r30718508 = a;
        double r30718509 = r30718505 - r30718508;
        double r30718510 = r30718507 / r30718509;
        double r30718511 = r30718504 * r30718510;
        double r30718512 = r30718503 + r30718511;
        return r30718512;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30718513 = x;
        double r30718514 = z;
        double r30718515 = t;
        double r30718516 = r30718514 - r30718515;
        double r30718517 = cbrt(r30718516);
        double r30718518 = a;
        double r30718519 = r30718514 - r30718518;
        double r30718520 = cbrt(r30718519);
        double r30718521 = r30718517 / r30718520;
        double r30718522 = r30718521 * r30718521;
        double r30718523 = y;
        double r30718524 = r30718522 * r30718523;
        double r30718525 = r30718524 * r30718521;
        double r30718526 = r30718513 + r30718525;
        return r30718526;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.4
Target1.3
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.0

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

  4. Applied add-cube-cbrt1.8

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

  5. Applied times-frac1.8

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

  6. Applied associate-*r*0.5

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

  7. Simplified0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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