Average Error: 1.4 → 0.7
Time: 17.9s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - a}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - a}} + x
double f(double x, double y, double z, double t, double a) {
        double r32235833 = x;
        double r32235834 = y;
        double r32235835 = z;
        double r32235836 = t;
        double r32235837 = r32235835 - r32235836;
        double r32235838 = a;
        double r32235839 = r32235835 - r32235838;
        double r32235840 = r32235837 / r32235839;
        double r32235841 = r32235834 * r32235840;
        double r32235842 = r32235833 + r32235841;
        return r32235842;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32235843 = y;
        double r32235844 = z;
        double r32235845 = a;
        double r32235846 = r32235844 - r32235845;
        double r32235847 = cbrt(r32235846);
        double r32235848 = t;
        double r32235849 = r32235844 - r32235848;
        double r32235850 = cbrt(r32235849);
        double r32235851 = r32235847 / r32235850;
        double r32235852 = r32235851 * r32235851;
        double r32235853 = r32235843 / r32235852;
        double r32235854 = cbrt(r32235850);
        double r32235855 = r32235850 * r32235850;
        double r32235856 = cbrt(r32235855);
        double r32235857 = r32235854 * r32235856;
        double r32235858 = r32235857 / r32235847;
        double r32235859 = r32235853 * r32235858;
        double r32235860 = x;
        double r32235861 = r32235859 + r32235860;
        return r32235861;
}

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
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied add-cube-cbrt1.9

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

  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*0.6

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

  7. Simplified0.5

    \[\leadsto x + \color{blue}{\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.6

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

  10. Applied cbrt-prod0.7

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

  11. Final simplification0.7

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

Reproduce

herbie shell --seed 2019171 
(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)))))