Average Error: 10.4 → 0.4
Time: 16.2s
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 r364290 = x;
        double r364291 = y;
        double r364292 = z;
        double r364293 = t;
        double r364294 = r364292 - r364293;
        double r364295 = r364291 * r364294;
        double r364296 = a;
        double r364297 = r364296 - r364293;
        double r364298 = r364295 / r364297;
        double r364299 = r364290 + r364298;
        return r364299;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r364300 = y;
        double r364301 = z;
        double r364302 = t;
        double r364303 = r364301 - r364302;
        double r364304 = r364300 * r364303;
        double r364305 = a;
        double r364306 = r364305 - r364302;
        double r364307 = r364304 / r364306;
        double r364308 = -7.132946171081901e+252;
        bool r364309 = r364307 <= r364308;
        double r364310 = 2.630221087213083e+284;
        bool r364311 = r364307 <= r364310;
        double r364312 = !r364311;
        bool r364313 = r364309 || r364312;
        double r364314 = x;
        double r364315 = r364303 / r364306;
        double r364316 = r364300 * r364315;
        double r364317 = r364314 + r364316;
        double r364318 = r364314 + r364307;
        double r364319 = r364313 ? r364317 : r364318;
        return r364319;
}

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))))