Average Error: 10.7 → 0.5
Time: 18.6s
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 r466686 = x;
        double r466687 = y;
        double r466688 = z;
        double r466689 = t;
        double r466690 = r466688 - r466689;
        double r466691 = r466687 * r466690;
        double r466692 = a;
        double r466693 = r466688 - r466692;
        double r466694 = r466691 / r466693;
        double r466695 = r466686 + r466694;
        return r466695;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r466696 = y;
        double r466697 = z;
        double r466698 = t;
        double r466699 = r466697 - r466698;
        double r466700 = r466696 * r466699;
        double r466701 = a;
        double r466702 = r466697 - r466701;
        double r466703 = r466700 / r466702;
        double r466704 = -4.663883987632394e+166;
        bool r466705 = r466703 <= r466704;
        double r466706 = 2.7311419804575177e+282;
        bool r466707 = r466703 <= r466706;
        double r466708 = !r466707;
        bool r466709 = r466705 || r466708;
        double r466710 = x;
        double r466711 = r466702 / r466699;
        double r466712 = r466696 / r466711;
        double r466713 = r466710 + r466712;
        double r466714 = r466710 + r466703;
        double r466715 = r466709 ? r466713 : r466714;
        return r466715;
}

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))))