Average Error: 1.3 → 0.4
Time: 15.9s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.168187031720985 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\ \mathbf{elif}\;y \le 1.5969460187838342 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.168187031720985 \cdot 10^{-13}:\\
\;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\

\mathbf{elif}\;y \le 1.5969460187838342 \cdot 10^{-22}:\\
\;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r12255837 = x;
        double r12255838 = y;
        double r12255839 = z;
        double r12255840 = t;
        double r12255841 = r12255839 - r12255840;
        double r12255842 = a;
        double r12255843 = r12255839 - r12255842;
        double r12255844 = r12255841 / r12255843;
        double r12255845 = r12255838 * r12255844;
        double r12255846 = r12255837 + r12255845;
        return r12255846;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r12255847 = y;
        double r12255848 = -8.168187031720985e-13;
        bool r12255849 = r12255847 <= r12255848;
        double r12255850 = x;
        double r12255851 = 1.0;
        double r12255852 = z;
        double r12255853 = a;
        double r12255854 = r12255852 - r12255853;
        double r12255855 = r12255851 / r12255854;
        double r12255856 = t;
        double r12255857 = r12255852 - r12255856;
        double r12255858 = r12255851 / r12255857;
        double r12255859 = r12255855 / r12255858;
        double r12255860 = r12255859 * r12255847;
        double r12255861 = r12255850 + r12255860;
        double r12255862 = 1.5969460187838342e-22;
        bool r12255863 = r12255847 <= r12255862;
        double r12255864 = r12255847 * r12255857;
        double r12255865 = r12255864 / r12255854;
        double r12255866 = r12255865 + r12255850;
        double r12255867 = r12255863 ? r12255866 : r12255861;
        double r12255868 = r12255849 ? r12255861 : r12255867;
        return r12255868;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -8.168187031720985e-13 or 1.5969460187838342e-22 < y

    1. Initial program 0.5

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

    3. Applied clear-num0.6

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv0.7

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

    6. Applied associate-/r*0.6

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

    if -8.168187031720985e-13 < y < 1.5969460187838342e-22

    1. Initial program 2.1

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

    3. Applied clear-num2.1

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/2.1

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

    6. Applied associate-*r*3.1

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

    7. Simplified3.1

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

    9. Applied associate-*l/0.2

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.168187031720985 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\ \mathbf{elif}\;y \le 1.5969460187838342 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{1}{z - t}} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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)))))