Average Error: 7.5 → 2.2
Time: 3.5s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\ \;\;\;\;1 \cdot \left(\left(y \cdot t\right) \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\
\;\;\;\;1 \cdot \left(\left(y \cdot t\right) \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r444877 = x;
        double r444878 = y;
        double r444879 = r444877 * r444878;
        double r444880 = z;
        double r444881 = r444880 * r444878;
        double r444882 = r444879 - r444881;
        double r444883 = t;
        double r444884 = r444882 * r444883;
        return r444884;
}
↓
double f(double x, double y, double z, double t) {
        double r444885 = x;
        double r444886 = y;
        double r444887 = r444885 * r444886;
        double r444888 = z;
        double r444889 = r444888 * r444886;
        double r444890 = r444887 - r444889;
        double r444891 = -1.8183640740776212e+283;
        bool r444892 = r444890 <= r444891;
        double r444893 = 1.0;
        double r444894 = t;
        double r444895 = r444886 * r444894;
        double r444896 = r444885 - r444888;
        double r444897 = r444895 * r444896;
        double r444898 = r444893 * r444897;
        double r444899 = 2.592867859186123e+96;
        bool r444900 = r444890 <= r444899;
        double r444901 = r444890 * r444894;
        double r444902 = r444896 * r444894;
        double r444903 = r444886 * r444902;
        double r444904 = r444900 ? r444901 : r444903;
        double r444905 = r444892 ? r444898 : r444904;
        return r444905;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.5
Target3.2
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -1.8183640740776212e+283

    1. Initial program 52.5

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--52.5

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

    4. Applied associate-*l*0.3

      \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt1.5

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

    7. Applied associate-*r*1.5

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

    9. Applied *-un-lft-identity1.5

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

    10. Applied associate-*l*1.5

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

    11. Simplified0.2

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

    if -1.8183640740776212e+283 < (- (* x y) (* z y)) < 2.592867859186123e+96

    1. Initial program 1.9

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    if 2.592867859186123e+96 < (- (* x y) (* z y))

    1. Initial program 17.0

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--17.0

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

    4. Applied associate-*l*4.1

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\ \;\;\;\;1 \cdot \left(\left(y \cdot t\right) \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))