Average Error: 10.9 → 0.9
Time: 16.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\
\;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r340898 = x;
        double r340899 = y;
        double r340900 = z;
        double r340901 = t;
        double r340902 = r340900 - r340901;
        double r340903 = r340899 * r340902;
        double r340904 = a;
        double r340905 = r340904 - r340901;
        double r340906 = r340903 / r340905;
        double r340907 = r340898 + r340906;
        return r340907;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r340908 = y;
        double r340909 = z;
        double r340910 = t;
        double r340911 = r340909 - r340910;
        double r340912 = r340908 * r340911;
        double r340913 = a;
        double r340914 = r340913 - r340910;
        double r340915 = r340912 / r340914;
        double r340916 = -8.221766270881261e+83;
        bool r340917 = r340915 <= r340916;
        double r340918 = x;
        double r340919 = r340908 / r340914;
        double r340920 = r340919 * r340911;
        double r340921 = r340918 + r340920;
        double r340922 = 3.6173472825315326e+225;
        bool r340923 = r340915 <= r340922;
        double r340924 = r340918 + r340915;
        double r340925 = r340914 / r340911;
        double r340926 = r340908 / r340925;
        double r340927 = r340918 + r340926;
        double r340928 = r340923 ? r340924 : r340927;
        double r340929 = r340917 ? r340921 : r340928;
        return r340929;
}

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

Original10.9
Target1.3
Herbie0.9
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) (- a t)) < -8.221766270881261e+83

    1. Initial program 30.5

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

    3. Applied associate-/l*2.6

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

    5. Applied associate-/r/3.2

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

    if -8.221766270881261e+83 < (/ (* y (- z t)) (- a t)) < 3.6173472825315326e+225

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

    7. Applied associate-*r/0.2

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

    if 3.6173472825315326e+225 < (/ (* y (- z t)) (- a t))

    1. Initial program 51.8

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

    3. Applied associate-/l*1.8

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))