Average Error: 10.7 → 0.5
Time: 18.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -4.663883987632393677861891411181961763687 \cdot 10^{166} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.731141980457517668001956254413700357633 \cdot 10^{282}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -4.663883987632393677861891411181961763687 \cdot 10^{166} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.731141980457517668001956254413700357633 \cdot 10^{282}\right):\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r479858 = x;
        double r479859 = y;
        double r479860 = z;
        double r479861 = t;
        double r479862 = r479860 - r479861;
        double r479863 = r479859 * r479862;
        double r479864 = a;
        double r479865 = r479860 - r479864;
        double r479866 = r479863 / r479865;
        double r479867 = r479858 + r479866;
        return r479867;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r479868 = y;
        double r479869 = z;
        double r479870 = t;
        double r479871 = r479869 - r479870;
        double r479872 = r479868 * r479871;
        double r479873 = a;
        double r479874 = r479869 - r479873;
        double r479875 = r479872 / r479874;
        double r479876 = -4.663883987632394e+166;
        bool r479877 = r479875 <= r479876;
        double r479878 = 2.7311419804575177e+282;
        bool r479879 = r479875 <= r479878;
        double r479880 = !r479879;
        bool r479881 = r479877 || r479880;
        double r479882 = x;
        double r479883 = r479874 / r479871;
        double r479884 = r479868 / r479883;
        double r479885 = r479882 + r479884;
        double r479886 = r479882 + r479875;
        double r479887 = r479881 ? r479885 : r479886;
        return r479887;
}

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

Original10.7
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- z a)) < -4.663883987632394e+166 or 2.7311419804575177e+282 < (/ (* y (- z t)) (- z a))

    1. Initial program 49.3

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

    3. Applied associate-/l*1.5

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

    if -4.663883987632394e+166 < (/ (* y (- z t)) (- z a)) < 2.7311419804575177e+282

    1. Initial program 0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -4.663883987632393677861891411181961763687 \cdot 10^{166} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.731141980457517668001956254413700357633 \cdot 10^{282}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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