Average Error: 6.1 → 1.1
Time: 18.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\ \;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\ \mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\
\;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\

\mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r17958775 = x;
        double r17958776 = y;
        double r17958777 = z;
        double r17958778 = t;
        double r17958779 = r17958777 - r17958778;
        double r17958780 = r17958776 * r17958779;
        double r17958781 = a;
        double r17958782 = r17958780 / r17958781;
        double r17958783 = r17958775 + r17958782;
        return r17958783;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r17958784 = y;
        double r17958785 = -1.7432637471506773e-180;
        bool r17958786 = r17958784 <= r17958785;
        double r17958787 = x;
        double r17958788 = z;
        double r17958789 = t;
        double r17958790 = r17958788 - r17958789;
        double r17958791 = a;
        double r17958792 = cbrt(r17958791);
        double r17958793 = r17958790 / r17958792;
        double r17958794 = r17958792 * r17958792;
        double r17958795 = r17958784 / r17958794;
        double r17958796 = r17958793 * r17958795;
        double r17958797 = r17958787 + r17958796;
        double r17958798 = 1.593765271222455e-09;
        bool r17958799 = r17958784 <= r17958798;
        double r17958800 = 1.0;
        double r17958801 = r17958784 * r17958790;
        double r17958802 = r17958791 / r17958801;
        double r17958803 = r17958800 / r17958802;
        double r17958804 = r17958787 + r17958803;
        double r17958805 = r17958791 / r17958790;
        double r17958806 = r17958784 / r17958805;
        double r17958807 = r17958787 + r17958806;
        double r17958808 = r17958799 ? r17958804 : r17958807;
        double r17958809 = r17958786 ? r17958797 : r17958808;
        return r17958809;
}

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
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.7432637471506773e-180

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.9

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

    4. Applied times-frac2.1

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

    if -1.7432637471506773e-180 < y < 1.593765271222455e-09

    1. Initial program 0.4

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

    3. Applied clear-num0.5

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

    if 1.593765271222455e-09 < y

    1. Initial program 14.4

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

    3. Applied associate-/l*0.7

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\ \;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\ \mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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