Average Error: 6.2 → 0.6
Time: 3.4s
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 r387819 = x;
        double r387820 = y;
        double r387821 = z;
        double r387822 = t;
        double r387823 = r387821 - r387822;
        double r387824 = r387820 * r387823;
        double r387825 = a;
        double r387826 = r387824 / r387825;
        double r387827 = r387819 + r387826;
        return r387827;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r387828 = y;
        double r387829 = z;
        double r387830 = t;
        double r387831 = r387829 - r387830;
        double r387832 = r387828 * r387831;
        double r387833 = a;
        double r387834 = r387832 / r387833;
        double r387835 = -inf.0;
        bool r387836 = r387834 <= r387835;
        double r387837 = x;
        double r387838 = r387831 / r387833;
        double r387839 = r387828 * r387838;
        double r387840 = r387837 + r387839;
        double r387841 = 5.011049390082959e+291;
        bool r387842 = r387834 <= r387841;
        double r387843 = r387837 + r387834;
        double r387844 = r387833 / r387831;
        double r387845 = r387828 / r387844;
        double r387846 = r387837 + r387845;
        double r387847 = r387842 ? r387843 : r387846;
        double r387848 = r387836 ? r387840 : r387847;
        return r387848;
}

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, E"
  :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)))