Average Error: 6.2 → 0.6
Time: 3.3s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -\infty:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.01104939008295895 \cdot 10^{291}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -\infty:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.01104939008295895 \cdot 10^{291}:\\
\;\;\;\;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 r375984 = x;
        double r375985 = y;
        double r375986 = z;
        double r375987 = t;
        double r375988 = r375986 - r375987;
        double r375989 = r375985 * r375988;
        double r375990 = a;
        double r375991 = r375989 / r375990;
        double r375992 = r375984 - r375991;
        return r375992;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r375993 = y;
        double r375994 = z;
        double r375995 = t;
        double r375996 = r375994 - r375995;
        double r375997 = r375993 * r375996;
        double r375998 = a;
        double r375999 = r375997 / r375998;
        double r376000 = -inf.0;
        bool r376001 = r375999 <= r376000;
        double r376002 = x;
        double r376003 = r375996 / r375998;
        double r376004 = r375993 * r376003;
        double r376005 = r376002 - r376004;
        double r376006 = 5.011049390082959e+291;
        bool r376007 = r375999 <= r376006;
        double r376008 = r376002 - r375999;
        double r376009 = r375998 / r375996;
        double r376010 = r375993 / r376009;
        double r376011 = r376002 - r376010;
        double r376012 = r376007 ? r376008 : r376011;
        double r376013 = r376001 ? r376005 : r376012;
        return r376013;
}

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
Target0.6
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) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.2

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

    5. Simplified0.2

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

    if -inf.0 < (/ (* y (- z t)) a) < 5.011049390082959e+291

    1. Initial program 0.4

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

    if 5.011049390082959e+291 < (/ (* y (- z t)) a)

    1. Initial program 54.0

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

    3. Applied associate-/l*4.3

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -\infty:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.01104939008295895 \cdot 10^{291}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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)))