Average Error: 6.0 → 0.8
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 4.0646321336868101 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \le 4.0646321336868101 \cdot 10^{-14}:\\
\;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r437876 = x;
        double r437877 = y;
        double r437878 = z;
        double r437879 = t;
        double r437880 = r437878 - r437879;
        double r437881 = r437877 * r437880;
        double r437882 = a;
        double r437883 = r437881 / r437882;
        double r437884 = r437876 + r437883;
        return r437884;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r437885 = y;
        double r437886 = -3.0637893463441613e+62;
        bool r437887 = r437885 <= r437886;
        double r437888 = x;
        double r437889 = a;
        double r437890 = z;
        double r437891 = t;
        double r437892 = r437890 - r437891;
        double r437893 = r437889 / r437892;
        double r437894 = r437885 / r437893;
        double r437895 = r437888 + r437894;
        double r437896 = 4.06463213368681e-14;
        bool r437897 = r437885 <= r437896;
        double r437898 = r437885 * r437890;
        double r437899 = -r437891;
        double r437900 = r437885 * r437899;
        double r437901 = r437898 + r437900;
        double r437902 = r437901 / r437889;
        double r437903 = r437888 + r437902;
        double r437904 = r437892 / r437889;
        double r437905 = r437885 * r437904;
        double r437906 = r437888 + r437905;
        double r437907 = r437897 ? r437903 : r437906;
        double r437908 = r437887 ? r437895 : r437907;
        return r437908;
}

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
Target0.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.0637893463441613e+62

    1. Initial program 18.9

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

    3. Applied associate-/l*1.1

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

    if -3.0637893463441613e+62 < y < 4.06463213368681e-14

    1. Initial program 0.8

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

    3. Applied sub-neg0.8

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

    4. Applied distribute-lft-in0.8

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

    if 4.06463213368681e-14 < y

    1. Initial program 14.1

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

    3. Applied *-un-lft-identity14.1

      \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{1 \cdot a}}\]

    4. Applied times-frac0.7

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - t}{a}}\]

    5. Simplified0.7

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 4.0646321336868101 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(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)))