Average Error: 1.3 → 0.5
Time: 15.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r29292782 = x;
        double r29292783 = y;
        double r29292784 = z;
        double r29292785 = t;
        double r29292786 = r29292784 - r29292785;
        double r29292787 = a;
        double r29292788 = r29292784 - r29292787;
        double r29292789 = r29292786 / r29292788;
        double r29292790 = r29292783 * r29292789;
        double r29292791 = r29292782 + r29292790;
        return r29292791;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29292792 = z;
        double r29292793 = t;
        double r29292794 = r29292792 - r29292793;
        double r29292795 = cbrt(r29292794);
        double r29292796 = r29292795 * r29292795;
        double r29292797 = a;
        double r29292798 = r29292792 - r29292797;
        double r29292799 = cbrt(r29292798);
        double r29292800 = r29292799 * r29292799;
        double r29292801 = r29292796 / r29292800;
        double r29292802 = y;
        double r29292803 = r29292799 / r29292795;
        double r29292804 = r29292802 / r29292803;
        double r29292805 = r29292801 * r29292804;
        double r29292806 = x;
        double r29292807 = r29292805 + r29292806;
        return r29292807;
}

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

Original1.3
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied associate-*r/11.2

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

  5. Applied associate-/l*1.2

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

  7. Applied add-cube-cbrt1.7

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

  8. Applied add-cube-cbrt1.6

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

  9. Applied times-frac1.6

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

  10. Applied *-un-lft-identity1.6

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

  11. Applied times-frac0.5

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

  12. Simplified0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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)))))