Average Error: 6.1 → 0.8
Time: 23.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.687887453796694071694322260841252701637 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 317581350695084538236343437351714816:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.687887453796694071694322260841252701637 \cdot 10^{-76}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;a \le 317581350695084538236343437351714816:\\
\;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r20363905 = x;
        double r20363906 = y;
        double r20363907 = z;
        double r20363908 = t;
        double r20363909 = r20363907 - r20363908;
        double r20363910 = r20363906 * r20363909;
        double r20363911 = a;
        double r20363912 = r20363910 / r20363911;
        double r20363913 = r20363905 + r20363912;
        return r20363913;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r20363914 = a;
        double r20363915 = -7.687887453796694e-76;
        bool r20363916 = r20363914 <= r20363915;
        double r20363917 = x;
        double r20363918 = y;
        double r20363919 = z;
        double r20363920 = t;
        double r20363921 = r20363919 - r20363920;
        double r20363922 = r20363914 / r20363921;
        double r20363923 = r20363918 / r20363922;
        double r20363924 = r20363917 + r20363923;
        double r20363925 = 3.1758135069508454e+35;
        bool r20363926 = r20363914 <= r20363925;
        double r20363927 = r20363921 * r20363918;
        double r20363928 = r20363927 / r20363914;
        double r20363929 = r20363928 + r20363917;
        double r20363930 = r20363926 ? r20363929 : r20363924;
        double r20363931 = r20363916 ? r20363924 : r20363930;
        return r20363931;
}

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

Original6.1
Target0.7
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -7.687887453796694e-76 or 3.1758135069508454e+35 < a

    1. Initial program 9.0

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

    3. Applied associate-/l*0.8

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

    if -7.687887453796694e-76 < a < 3.1758135069508454e+35

    1. Initial program 0.8

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

    2. Taylor expanded around 0 0.8

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

    3. Simplified3.9

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}\]
    4. Using strategy rm

    5. Applied associate-*r/0.8

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.687887453796694071694322260841252701637 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 317581350695084538236343437351714816:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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