Average Error: 6.9 → 3.0
Time: 2.9s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.049647329143563 \cdot 10^{27} \lor \neg \left(y \le 1.1333992022375297 \cdot 10^{48}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.049647329143563 \cdot 10^{27} \lor \neg \left(y \le 1.1333992022375297 \cdot 10^{48}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1351817 = x;
        double r1351818 = y;
        double r1351819 = r1351817 * r1351818;
        double r1351820 = z;
        double r1351821 = r1351820 * r1351818;
        double r1351822 = r1351819 - r1351821;
        double r1351823 = t;
        double r1351824 = r1351822 * r1351823;
        return r1351824;
}
↓
double f(double x, double y, double z, double t) {
        double r1351825 = y;
        double r1351826 = -4.049647329143563e+27;
        bool r1351827 = r1351825 <= r1351826;
        double r1351828 = 1.1333992022375297e+48;
        bool r1351829 = r1351825 <= r1351828;
        double r1351830 = !r1351829;
        bool r1351831 = r1351827 || r1351830;
        double r1351832 = t;
        double r1351833 = r1351832 * r1351825;
        double r1351834 = x;
        double r1351835 = z;
        double r1351836 = r1351834 - r1351835;
        double r1351837 = r1351833 * r1351836;
        double r1351838 = r1351825 * r1351836;
        double r1351839 = r1351832 * r1351838;
        double r1351840 = r1351831 ? r1351837 : r1351839;
        return r1351840;
}

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

Original6.9
Target2.9
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.049647329143563e+27 or 1.1333992022375297e+48 < y

    1. Initial program 17.2

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

    2. Simplified17.2

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

    4. Applied associate-*r*4.4

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

    if -4.049647329143563e+27 < y < 1.1333992022375297e+48

    1. Initial program 2.3

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

    2. Simplified2.3

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

    4. Applied associate-*r*7.5

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

    6. Applied associate-*l*2.3

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(x - z\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.049647329143563 \cdot 10^{27} \lor \neg \left(y \le 1.1333992022375297 \cdot 10^{48}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))