Average Error: 6.1 → 1.1
Time: 18.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -3.273801318257331161706233360861922033076 \cdot 10^{273}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le -8.544258254814858046435073701156046376542 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\sqrt[3]{a}} \cdot \left(\left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}}{\sqrt[3]{a}}\right)\\ \end{array}\]
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}:\\
\;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\

\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 r16058768 = x;
        double r16058769 = y;
        double r16058770 = z;
        double r16058771 = t;
        double r16058772 = r16058770 - r16058771;
        double r16058773 = r16058769 * r16058772;
        double r16058774 = a;
        double r16058775 = r16058773 / r16058774;
        double r16058776 = r16058768 - r16058775;
        return r16058776;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r16058777 = z;
        double r16058778 = t;
        double r16058779 = r16058777 - r16058778;
        double r16058780 = y;
        double r16058781 = r16058779 * r16058780;
        double r16058782 = -3.273801318257331e+273;
        bool r16058783 = r16058781 <= r16058782;
        double r16058784 = x;
        double r16058785 = a;
        double r16058786 = r16058785 / r16058779;
        double r16058787 = r16058780 / r16058786;
        double r16058788 = r16058784 - r16058787;
        double r16058789 = -8.544258254814858e-245;
        bool r16058790 = r16058781 <= r16058789;
        double r16058791 = r16058781 / r16058785;
        double r16058792 = r16058784 - r16058791;
        double r16058793 = 1.0;
        double r16058794 = cbrt(r16058785);
        double r16058795 = r16058793 / r16058794;
        double r16058796 = cbrt(r16058780);
        double r16058797 = r16058796 / r16058794;
        double r16058798 = r16058779 * r16058797;
        double r16058799 = r16058796 * r16058796;
        double r16058800 = r16058796 * r16058799;
        double r16058801 = cbrt(r16058800);
        double r16058802 = r16058796 * r16058801;
        double r16058803 = r16058802 / r16058794;
        double r16058804 = r16058798 * r16058803;
        double r16058805 = r16058795 * r16058804;
        double r16058806 = r16058784 - r16058805;
        double r16058807 = r16058790 ? r16058792 : r16058806;
        double r16058808 = r16058783 ? r16058788 : r16058807;
        return r16058808;
}

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

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

  4. Final simplification1.1

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

Reproduce

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

  :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)))