Average Error: 11.3 → 0.6
Time: 3.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.7824488815679915 \cdot 10^{176}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.7824488815679915 \cdot 10^{176}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r645353 = x;
        double r645354 = y;
        double r645355 = z;
        double r645356 = t;
        double r645357 = r645355 - r645356;
        double r645358 = r645354 * r645357;
        double r645359 = a;
        double r645360 = r645355 - r645359;
        double r645361 = r645358 / r645360;
        double r645362 = r645353 + r645361;
        return r645362;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r645363 = y;
        double r645364 = z;
        double r645365 = t;
        double r645366 = r645364 - r645365;
        double r645367 = r645363 * r645366;
        double r645368 = a;
        double r645369 = r645364 - r645368;
        double r645370 = r645367 / r645369;
        double r645371 = -inf.0;
        bool r645372 = r645370 <= r645371;
        double r645373 = 2.7824488815679915e+176;
        bool r645374 = r645370 <= r645373;
        double r645375 = !r645374;
        bool r645376 = r645372 || r645375;
        double r645377 = x;
        double r645378 = r645366 / r645369;
        double r645379 = r645363 * r645378;
        double r645380 = r645377 + r645379;
        double r645381 = 1.0;
        double r645382 = r645381 / r645369;
        double r645383 = r645367 * r645382;
        double r645384 = r645377 + r645383;
        double r645385 = r645376 ? r645380 : r645384;
        return r645385;
}

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

Original11.3
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 2.7824488815679915e+176 < (/ (* y (- z t)) (- z a))

    1. Initial program 53.4

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

    3. Applied *-un-lft-identity53.4

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -inf.0 < (/ (* y (- z t)) (- z a)) < 2.7824488815679915e+176

    1. Initial program 0.3

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

    3. Applied div-inv0.3

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 2.7824488815679915 \cdot 10^{176}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))))