Average Error: 6.4 → 0.4
Time: 3.9s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.361987298119512454986754907617398197992 \cdot 10^{224}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x - \frac{y \cdot \left(z - t\right)}{a}\right)}^{1}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.361987298119512454986754907617398197992 \cdot 10^{224}\right):\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{else}:\\
\;\;\;\;{\left(x - \frac{y \cdot \left(z - t\right)}{a}\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r312911 = x;
        double r312912 = y;
        double r312913 = z;
        double r312914 = t;
        double r312915 = r312913 - r312914;
        double r312916 = r312912 * r312915;
        double r312917 = a;
        double r312918 = r312916 / r312917;
        double r312919 = r312911 - r312918;
        return r312919;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r312920 = y;
        double r312921 = z;
        double r312922 = t;
        double r312923 = r312921 - r312922;
        double r312924 = r312920 * r312923;
        double r312925 = -2.8851274379852167e+296;
        bool r312926 = r312924 <= r312925;
        double r312927 = 1.3619872981195125e+224;
        bool r312928 = r312924 <= r312927;
        double r312929 = !r312928;
        bool r312930 = r312926 || r312929;
        double r312931 = x;
        double r312932 = a;
        double r312933 = r312920 / r312932;
        double r312934 = r312933 * r312923;
        double r312935 = r312931 - r312934;
        double r312936 = r312924 / r312932;
        double r312937 = r312931 - r312936;
        double r312938 = 1.0;
        double r312939 = pow(r312937, r312938);
        double r312940 = r312930 ? r312935 : r312939;
        return r312940;
}

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

Original6.4
Target0.7
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -2.8851274379852167e+296 or 1.3619872981195125e+224 < (* y (- z t))

    1. Initial program 43.3

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

    3. Applied associate-/l*0.4

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.5

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

    if -2.8851274379852167e+296 < (* y (- z t)) < 1.3619872981195125e+224

    1. Initial program 0.4

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

    3. Applied pow10.4

      \[\leadsto \color{blue}{{\left(x - \frac{y \cdot \left(z - t\right)}{a}\right)}^{1}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.361987298119512454986754907617398197992 \cdot 10^{224}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x - \frac{y \cdot \left(z - t\right)}{a}\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(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)))