Average Error: 6.0 → 0.5
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.590048754587910739584683033042450323901 \cdot 10^{302}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.496936338455672195431667619657047124773 \cdot 10^{156}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -7.590048754587910739584683033042450323901 \cdot 10^{302}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.496936338455672195431667619657047124773 \cdot 10^{156}:\\
\;\;\;\;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 r232967 = x;
        double r232968 = y;
        double r232969 = z;
        double r232970 = t;
        double r232971 = r232969 - r232970;
        double r232972 = r232968 * r232971;
        double r232973 = a;
        double r232974 = r232972 / r232973;
        double r232975 = r232967 + r232974;
        return r232975;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r232976 = y;
        double r232977 = z;
        double r232978 = t;
        double r232979 = r232977 - r232978;
        double r232980 = r232976 * r232979;
        double r232981 = -7.59004875458791e+302;
        bool r232982 = r232980 <= r232981;
        double r232983 = x;
        double r232984 = a;
        double r232985 = r232977 / r232984;
        double r232986 = r232978 / r232984;
        double r232987 = r232985 - r232986;
        double r232988 = r232976 * r232987;
        double r232989 = r232983 + r232988;
        double r232990 = 1.4969363384556722e+156;
        bool r232991 = r232980 <= r232990;
        double r232992 = r232980 / r232984;
        double r232993 = r232983 + r232992;
        double r232994 = r232984 / r232979;
        double r232995 = r232976 / r232994;
        double r232996 = r232983 + r232995;
        double r232997 = r232991 ? r232993 : r232996;
        double r232998 = r232982 ? r232989 : r232997;
        return r232998;
}

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

Original6.0
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -7.59004875458791e+302

    1. Initial program 61.5

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

    3. Applied add-cube-cbrt61.6

      \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

    4. Applied times-frac1.1

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}}\]

    5. Taylor expanded around 0 61.5

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

    6. Simplified0.2

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

    if -7.59004875458791e+302 < (* y (- z t)) < 1.4969363384556722e+156

    1. Initial program 0.4

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

    if 1.4969363384556722e+156 < (* y (- z t))

    1. Initial program 21.7

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

    3. Applied associate-/l*1.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.590048754587910739584683033042450323901 \cdot 10^{302}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.496936338455672195431667619657047124773 \cdot 10^{156}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))