Average Error: 6.4 → 2.5
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r269920 = x;
        double r269921 = y;
        double r269922 = z;
        double r269923 = t;
        double r269924 = r269922 - r269923;
        double r269925 = r269921 * r269924;
        double r269926 = a;
        double r269927 = r269925 / r269926;
        double r269928 = r269920 + r269927;
        return r269928;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r269929 = z;
        double r269930 = -2.7878949931611257e-291;
        bool r269931 = r269929 <= r269930;
        double r269932 = 4.7957580216954454e-235;
        bool r269933 = r269929 <= r269932;
        double r269934 = !r269933;
        bool r269935 = r269931 || r269934;
        double r269936 = x;
        double r269937 = y;
        double r269938 = a;
        double r269939 = r269937 / r269938;
        double r269940 = t;
        double r269941 = r269929 - r269940;
        double r269942 = r269939 * r269941;
        double r269943 = r269936 + r269942;
        double r269944 = r269938 / r269941;
        double r269945 = r269937 / r269944;
        double r269946 = r269936 + r269945;
        double r269947 = r269935 ? r269943 : r269946;
        return r269947;
}

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
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.7878949931611257e-291 or 4.7957580216954454e-235 < z

    1. Initial program 6.6

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

    3. Applied associate-/l*5.6

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

    5. Applied associate-/r/2.3

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

    if -2.7878949931611257e-291 < z < 4.7957580216954454e-235

    1. Initial program 4.3

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

    3. Applied associate-/l*5.1

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))