Average Error: 6.1 → 1.1
Time: 17.9s
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 r15842822 = x;
        double r15842823 = y;
        double r15842824 = z;
        double r15842825 = t;
        double r15842826 = r15842824 - r15842825;
        double r15842827 = r15842823 * r15842826;
        double r15842828 = a;
        double r15842829 = r15842827 / r15842828;
        double r15842830 = r15842822 + r15842829;
        return r15842830;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15842831 = y;
        double r15842832 = -1.7432637471506773e-180;
        bool r15842833 = r15842831 <= r15842832;
        double r15842834 = x;
        double r15842835 = z;
        double r15842836 = t;
        double r15842837 = r15842835 - r15842836;
        double r15842838 = a;
        double r15842839 = cbrt(r15842838);
        double r15842840 = r15842837 / r15842839;
        double r15842841 = r15842839 * r15842839;
        double r15842842 = r15842831 / r15842841;
        double r15842843 = r15842840 * r15842842;
        double r15842844 = r15842834 + r15842843;
        double r15842845 = 1.593765271222455e-09;
        bool r15842846 = r15842831 <= r15842845;
        double r15842847 = 1.0;
        double r15842848 = r15842831 * r15842837;
        double r15842849 = r15842838 / r15842848;
        double r15842850 = r15842847 / r15842849;
        double r15842851 = r15842834 + r15842850;
        double r15842852 = r15842838 / r15842837;
        double r15842853 = r15842831 / r15842852;
        double r15842854 = r15842834 + r15842853;
        double r15842855 = r15842846 ? r15842851 : r15842854;
        double r15842856 = r15842833 ? r15842844 : r15842855;
        return r15842856;
}

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)))