Average Error: 6.1 → 1.8
Time: 16.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(z - t\right) \cdot y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\
\;\;\;\;\frac{1}{\frac{a}{\left(z - t\right) \cdot y}} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r16348900 = x;
        double r16348901 = y;
        double r16348902 = z;
        double r16348903 = t;
        double r16348904 = r16348902 - r16348903;
        double r16348905 = r16348901 * r16348904;
        double r16348906 = a;
        double r16348907 = r16348905 / r16348906;
        double r16348908 = r16348900 + r16348907;
        return r16348908;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r16348909 = a;
        double r16348910 = -1.7970758753613627e+105;
        bool r16348911 = r16348909 <= r16348910;
        double r16348912 = x;
        double r16348913 = y;
        double r16348914 = z;
        double r16348915 = t;
        double r16348916 = r16348914 - r16348915;
        double r16348917 = r16348916 / r16348909;
        double r16348918 = r16348913 * r16348917;
        double r16348919 = r16348912 + r16348918;
        double r16348920 = 1.2591825253525602e-146;
        bool r16348921 = r16348909 <= r16348920;
        double r16348922 = 1.0;
        double r16348923 = r16348916 * r16348913;
        double r16348924 = r16348909 / r16348923;
        double r16348925 = r16348922 / r16348924;
        double r16348926 = r16348925 + r16348912;
        double r16348927 = cbrt(r16348909);
        double r16348928 = r16348927 * r16348927;
        double r16348929 = r16348913 / r16348928;
        double r16348930 = r16348916 / r16348927;
        double r16348931 = r16348929 * r16348930;
        double r16348932 = r16348912 + r16348931;
        double r16348933 = r16348921 ? r16348926 : r16348932;
        double r16348934 = r16348911 ? r16348919 : r16348933;
        return r16348934;
}

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
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.7970758753613627e+105

    1. Initial program 11.2

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

    3. Applied *-un-lft-identity11.2

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -1.7970758753613627e+105 < a < 1.2591825253525602e-146

    1. Initial program 2.0

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

    3. Applied clear-num2.1

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

    if 1.2591825253525602e-146 < a

    1. Initial program 7.0

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

    3. Applied add-cube-cbrt7.5

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

    4. Applied times-frac2.1

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(z - t\right) \cdot y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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)))