Average Error: 5.9 → 1.3
Time: 6.6s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.7077180361223938 \cdot 10^{171}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.8014363335745625 \cdot 10^{72}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -5.7077180361223938 \cdot 10^{171}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.8014363335745625 \cdot 10^{72}:\\
\;\;\;\;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 r432279 = x;
        double r432280 = y;
        double r432281 = z;
        double r432282 = t;
        double r432283 = r432281 - r432282;
        double r432284 = r432280 * r432283;
        double r432285 = a;
        double r432286 = r432284 / r432285;
        double r432287 = r432279 - r432286;
        return r432287;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r432288 = y;
        double r432289 = z;
        double r432290 = t;
        double r432291 = r432289 - r432290;
        double r432292 = r432288 * r432291;
        double r432293 = -5.707718036122394e+171;
        bool r432294 = r432292 <= r432293;
        double r432295 = x;
        double r432296 = a;
        double r432297 = r432291 / r432296;
        double r432298 = r432288 * r432297;
        double r432299 = r432295 - r432298;
        double r432300 = 1.8014363335745625e+72;
        bool r432301 = r432292 <= r432300;
        double r432302 = r432292 / r432296;
        double r432303 = r432295 - r432302;
        double r432304 = r432296 / r432291;
        double r432305 = r432288 / r432304;
        double r432306 = r432295 - r432305;
        double r432307 = r432301 ? r432303 : r432306;
        double r432308 = r432294 ? r432299 : r432307;
        return r432308;
}

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

Original5.9
Target0.8
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -5.707718036122394e+171

    1. Initial program 23.8

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

    3. Applied *-un-lft-identity23.8

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -5.707718036122394e+171 < (* y (- z t)) < 1.8014363335745625e+72

    1. Initial program 0.5

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

    if 1.8014363335745625e+72 < (* y (- z t))

    1. Initial program 13.8

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

    3. Applied associate-/l*4.0

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.7077180361223938 \cdot 10^{171}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.8014363335745625 \cdot 10^{72}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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)))