Average Error: 11.0 → 0.3
Time: 5.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -5.7605669624172336 \cdot 10^{285} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.013977722943551 \cdot 10^{307}\right):\\ \;\;\;\;x + \frac{y}{\frac{1}{\frac{z - t}{z - a}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
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 -5.7605669624172336 \cdot 10^{285} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.013977722943551 \cdot 10^{307}\right):\\
\;\;\;\;x + \frac{y}{\frac{1}{\frac{z - t}{z - a}}}\\

\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 r553321 = x;
        double r553322 = y;
        double r553323 = z;
        double r553324 = t;
        double r553325 = r553323 - r553324;
        double r553326 = r553322 * r553325;
        double r553327 = a;
        double r553328 = r553323 - r553327;
        double r553329 = r553326 / r553328;
        double r553330 = r553321 + r553329;
        return r553330;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r553331 = y;
        double r553332 = z;
        double r553333 = t;
        double r553334 = r553332 - r553333;
        double r553335 = r553331 * r553334;
        double r553336 = a;
        double r553337 = r553332 - r553336;
        double r553338 = r553335 / r553337;
        double r553339 = -5.760566962417234e+285;
        bool r553340 = r553338 <= r553339;
        double r553341 = 2.013977722943551e+307;
        bool r553342 = r553338 <= r553341;
        double r553343 = !r553342;
        bool r553344 = r553340 || r553343;
        double r553345 = x;
        double r553346 = 1.0;
        double r553347 = r553334 / r553337;
        double r553348 = r553346 / r553347;
        double r553349 = r553331 / r553348;
        double r553350 = r553345 + r553349;
        double r553351 = r553345 + r553338;
        double r553352 = r553344 ? r553350 : r553351;
        return r553352;
}

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

Original11.0
Target1.1
Herbie0.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- z a)) < -5.760566962417234e+285 or 2.013977722943551e+307 < (/ (* y (- z t)) (- z a))

    1. Initial program 61.9

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

    3. Applied associate-/l*0.5

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

    5. Applied clear-num0.5

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

    if -5.760566962417234e+285 < (/ (* y (- z t)) (- z a)) < 2.013977722943551e+307

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -5.7605669624172336 \cdot 10^{285} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.013977722943551 \cdot 10^{307}\right):\\ \;\;\;\;x + \frac{y}{\frac{1}{\frac{z - t}{z - a}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))))