Average Error: 10.4 → 1.1
Time: 17.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r384892 = x;
        double r384893 = y;
        double r384894 = z;
        double r384895 = t;
        double r384896 = r384894 - r384895;
        double r384897 = r384893 * r384896;
        double r384898 = a;
        double r384899 = r384898 - r384895;
        double r384900 = r384897 / r384899;
        double r384901 = r384892 + r384900;
        return r384901;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r384902 = x;
        double r384903 = y;
        double r384904 = cbrt(r384903);
        double r384905 = r384904 * r384904;
        double r384906 = a;
        double r384907 = t;
        double r384908 = r384906 - r384907;
        double r384909 = cbrt(r384908);
        double r384910 = r384909 * r384909;
        double r384911 = r384905 / r384910;
        double r384912 = z;
        double r384913 = r384912 - r384907;
        double r384914 = r384909 / r384913;
        double r384915 = r384904 / r384914;
        double r384916 = r384911 * r384915;
        double r384917 = r384902 + r384916;
        return r384917;
}

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

Original10.4
Target1.2
Herbie1.1
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.2

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.2

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

    \[\leadsto x + \frac{y}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}}\]

  8. Applied add-cube-cbrt1.8

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

  9. Applied times-frac1.1

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}}\]

  10. Simplified1.1

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

  11. Final simplification1.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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