Average Error: 10.6 → 0.3
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.11675203590587826 \cdot 10^{282}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.11675203590587826 \cdot 10^{282}\right):\\
\;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\

\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 r533316 = x;
        double r533317 = y;
        double r533318 = z;
        double r533319 = t;
        double r533320 = r533318 - r533319;
        double r533321 = r533317 * r533320;
        double r533322 = a;
        double r533323 = r533322 - r533319;
        double r533324 = r533321 / r533323;
        double r533325 = r533316 + r533324;
        return r533325;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r533326 = y;
        double r533327 = z;
        double r533328 = t;
        double r533329 = r533327 - r533328;
        double r533330 = r533326 * r533329;
        double r533331 = a;
        double r533332 = r533331 - r533328;
        double r533333 = r533330 / r533332;
        double r533334 = -inf.0;
        bool r533335 = r533333 <= r533334;
        double r533336 = 3.1167520359058783e+282;
        bool r533337 = r533333 <= r533336;
        double r533338 = !r533337;
        bool r533339 = r533335 || r533338;
        double r533340 = r533332 / r533326;
        double r533341 = r533329 / r533340;
        double r533342 = x;
        double r533343 = r533341 + r533342;
        double r533344 = r533342 + r533333;
        double r533345 = r533339 ? r533343 : r533344;
        return r533345;
}

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

Original10.6
Target1.3
Herbie0.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 3.1167520359058783e+282 < (/ (* y (- z t)) (- a t))

    1. Initial program 62.0

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

    2. Simplified0.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num0.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef0.7

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

    7. Simplified0.6

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 3.1167520359058783e+282

    1. Initial program 0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.11675203590587826 \cdot 10^{282}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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))))