Average Error: 6.1 → 1.1
Time: 18.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -3.273801318257331161706233360861922033076 \cdot 10^{273}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le -8.544258254814858046435073701156046376542 \cdot 10^{-245}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\sqrt[3]{a}} \cdot \left(\left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}}{\sqrt[3]{a}}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\left(z - t\right) \cdot y \le -3.273801318257331161706233360861922033076 \cdot 10^{273}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;\left(z - t\right) \cdot y \le -8.544258254814858046435073701156046376542 \cdot 10^{-245}:\\
\;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{\sqrt[3]{a}} \cdot \left(\left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}}{\sqrt[3]{a}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r18242818 = x;
        double r18242819 = y;
        double r18242820 = z;
        double r18242821 = t;
        double r18242822 = r18242820 - r18242821;
        double r18242823 = r18242819 * r18242822;
        double r18242824 = a;
        double r18242825 = r18242823 / r18242824;
        double r18242826 = r18242818 + r18242825;
        return r18242826;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r18242827 = z;
        double r18242828 = t;
        double r18242829 = r18242827 - r18242828;
        double r18242830 = y;
        double r18242831 = r18242829 * r18242830;
        double r18242832 = -3.273801318257331e+273;
        bool r18242833 = r18242831 <= r18242832;
        double r18242834 = x;
        double r18242835 = a;
        double r18242836 = r18242835 / r18242829;
        double r18242837 = r18242830 / r18242836;
        double r18242838 = r18242834 + r18242837;
        double r18242839 = -8.544258254814858e-245;
        bool r18242840 = r18242831 <= r18242839;
        double r18242841 = r18242831 / r18242835;
        double r18242842 = r18242841 + r18242834;
        double r18242843 = 1.0;
        double r18242844 = cbrt(r18242835);
        double r18242845 = r18242843 / r18242844;
        double r18242846 = cbrt(r18242830);
        double r18242847 = r18242846 / r18242844;
        double r18242848 = r18242829 * r18242847;
        double r18242849 = r18242846 * r18242846;
        double r18242850 = r18242846 * r18242849;
        double r18242851 = cbrt(r18242850);
        double r18242852 = r18242846 * r18242851;
        double r18242853 = r18242852 / r18242844;
        double r18242854 = r18242848 * r18242853;
        double r18242855 = r18242845 * r18242854;
        double r18242856 = r18242834 + r18242855;
        double r18242857 = r18242840 ? r18242842 : r18242856;
        double r18242858 = r18242833 ? r18242838 : r18242857;
        return r18242858;
}

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

Original6.1
Target0.6
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -3.273801318257331e+273

    1. Initial program 48.2

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

    3. Applied associate-/l*0.2

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

    if -3.273801318257331e+273 < (* y (- z t)) < -8.544258254814858e-245

    1. Initial program 0.1

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

    if -8.544258254814858e-245 < (* y (- z t))

    1. Initial program 5.8

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

    3. Applied add-cube-cbrt6.3

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

    4. Applied times-frac3.0

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

    6. Applied div-inv3.0

      \[\leadsto x + \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}\]

    7. Applied associate-*r*2.7

      \[\leadsto x + \color{blue}{\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \left(z - t\right)\right) \cdot \frac{1}{\sqrt[3]{a}}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt2.9

      \[\leadsto x + \left(\frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \left(z - t\right)\right) \cdot \frac{1}{\sqrt[3]{a}}\]

    10. Applied times-frac2.9

      \[\leadsto x + \left(\color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right)} \cdot \left(z - t\right)\right) \cdot \frac{1}{\sqrt[3]{a}}\]

    11. Applied associate-*l*1.9

      \[\leadsto x + \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right)\right)} \cdot \frac{1}{\sqrt[3]{a}}\]
    12. Using strategy rm

    13. Applied add-cbrt-cube1.9

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -3.273801318257331161706233360861922033076 \cdot 10^{273}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le -8.544258254814858046435073701156046376542 \cdot 10^{-245}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\sqrt[3]{a}} \cdot \left(\left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}}{\sqrt[3]{a}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))