Average Error: 6.2 → 0.6
Time: 7.3s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -4.7670371624464174 \cdot 10^{302}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.18372496395244078 \cdot 10^{304}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -4.7670371624464174 \cdot 10^{302}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.18372496395244078 \cdot 10^{304}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r201316 = x;
        double r201317 = y;
        double r201318 = z;
        double r201319 = t;
        double r201320 = r201318 - r201319;
        double r201321 = r201317 * r201320;
        double r201322 = a;
        double r201323 = r201321 / r201322;
        double r201324 = r201316 - r201323;
        return r201324;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r201325 = y;
        double r201326 = z;
        double r201327 = t;
        double r201328 = r201326 - r201327;
        double r201329 = r201325 * r201328;
        double r201330 = a;
        double r201331 = r201329 / r201330;
        double r201332 = -4.7670371624464174e+302;
        bool r201333 = r201331 <= r201332;
        double r201334 = x;
        double r201335 = r201328 / r201330;
        double r201336 = r201325 * r201335;
        double r201337 = r201334 - r201336;
        double r201338 = 1.1837249639524408e+304;
        bool r201339 = r201331 <= r201338;
        double r201340 = r201334 - r201331;
        double r201341 = r201330 / r201328;
        double r201342 = r201325 / r201341;
        double r201343 = r201334 - r201342;
        double r201344 = r201339 ? r201340 : r201343;
        double r201345 = r201333 ? r201337 : r201344;
        return r201345;
}

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

Original6.2
Target0.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) a) < -4.7670371624464174e+302

    1. Initial program 60.4

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

    3. Applied *-un-lft-identity60.4

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

    4. Applied times-frac2.1

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

    5. Simplified2.1

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

    if -4.7670371624464174e+302 < (/ (* y (- z t)) a) < 1.1837249639524408e+304

    1. Initial program 0.4

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

    if 1.1837249639524408e+304 < (/ (* y (- z t)) a)

    1. Initial program 60.6

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

    3. Applied associate-/l*2.0

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -4.7670371624464174 \cdot 10^{302}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.18372496395244078 \cdot 10^{304}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))