Average Error: 10.4 → 0.4
Time: 14.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -7.132946171081901363675286218556549788265 \cdot 10^{252} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 2.630221087213082847268921436681766470379 \cdot 10^{284}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
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 -7.132946171081901363675286218556549788265 \cdot 10^{252} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 2.630221087213082847268921436681766470379 \cdot 10^{284}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r364624 = x;
        double r364625 = y;
        double r364626 = z;
        double r364627 = t;
        double r364628 = r364626 - r364627;
        double r364629 = r364625 * r364628;
        double r364630 = a;
        double r364631 = r364630 - r364627;
        double r364632 = r364629 / r364631;
        double r364633 = r364624 + r364632;
        return r364633;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r364634 = y;
        double r364635 = z;
        double r364636 = t;
        double r364637 = r364635 - r364636;
        double r364638 = r364634 * r364637;
        double r364639 = a;
        double r364640 = r364639 - r364636;
        double r364641 = r364638 / r364640;
        double r364642 = -7.132946171081901e+252;
        bool r364643 = r364641 <= r364642;
        double r364644 = 2.630221087213083e+284;
        bool r364645 = r364641 <= r364644;
        double r364646 = !r364645;
        bool r364647 = r364643 || r364646;
        double r364648 = x;
        double r364649 = r364637 / r364640;
        double r364650 = r364634 * r364649;
        double r364651 = r364648 + r364650;
        double r364652 = r364648 + r364641;
        double r364653 = r364647 ? r364651 : r364652;
        return r364653;
}

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

Original10.4
Target1.5
Herbie0.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -7.132946171081901e+252 or 2.630221087213083e+284 < (/ (* y (- z t)) (- a t))

    1. Initial program 56.8

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

    3. Applied *-un-lft-identity56.8

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

    4. Applied times-frac1.5

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

    5. Simplified1.5

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

    if -7.132946171081901e+252 < (/ (* y (- z t)) (- a t)) < 2.630221087213083e+284

    1. Initial program 0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -7.132946171081901363675286218556549788265 \cdot 10^{252} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 2.630221087213082847268921436681766470379 \cdot 10^{284}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))