Average Error: 6.2 → 0.7
Time: 4.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.8901331428127535 \cdot 10^{38}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \mathbf{elif}\;y \le 1.46766470083811 \cdot 10^{31}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.8901331428127535 \cdot 10^{38}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\

\mathbf{elif}\;y \le 1.46766470083811 \cdot 10^{31}:\\
\;\;\;\;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 r345860 = x;
        double r345861 = y;
        double r345862 = z;
        double r345863 = t;
        double r345864 = r345862 - r345863;
        double r345865 = r345861 * r345864;
        double r345866 = a;
        double r345867 = r345865 / r345866;
        double r345868 = r345860 + r345867;
        return r345868;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r345869 = y;
        double r345870 = -3.8901331428127535e+38;
        bool r345871 = r345869 <= r345870;
        double r345872 = x;
        double r345873 = z;
        double r345874 = a;
        double r345875 = r345873 / r345874;
        double r345876 = t;
        double r345877 = r345876 / r345874;
        double r345878 = r345875 - r345877;
        double r345879 = r345869 * r345878;
        double r345880 = r345872 + r345879;
        double r345881 = 1.46766470083811e+31;
        bool r345882 = r345869 <= r345881;
        double r345883 = r345873 - r345876;
        double r345884 = r345869 * r345883;
        double r345885 = r345884 / r345874;
        double r345886 = r345872 + r345885;
        double r345887 = r345874 / r345883;
        double r345888 = r345869 / r345887;
        double r345889 = r345872 + r345888;
        double r345890 = r345882 ? r345886 : r345889;
        double r345891 = r345871 ? r345880 : r345890;
        return r345891;
}

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

Original6.2
Target0.7
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.8901331428127535e+38

    1. Initial program 18.0

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

    3. Applied add-cube-cbrt18.4

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

    4. Applied times-frac2.6

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt2.7

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

    7. Applied times-frac2.7

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

    8. Applied associate-*l*1.1

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

    9. Taylor expanded around 0 18.0

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

    10. Simplified0.8

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

    if -3.8901331428127535e+38 < y < 1.46766470083811e+31

    1. Initial program 0.6

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

    if 1.46766470083811e+31 < y

    1. Initial program 17.2

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

    3. Applied associate-/l*1.1

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.8901331428127535 \cdot 10^{38}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \mathbf{elif}\;y \le 1.46766470083811 \cdot 10^{31}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 
(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)))