Average Error: 6.7 → 1.3
Time: 4.2s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -6.5003455406364965 \cdot 10^{272} \lor \neg \left(x \cdot y - z \cdot y \le 6.6662776022917816 \cdot 10^{272}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -6.5003455406364965 \cdot 10^{272} \lor \neg \left(x \cdot y - z \cdot y \le 6.6662776022917816 \cdot 10^{272}\right):\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r599892 = x;
        double r599893 = y;
        double r599894 = r599892 * r599893;
        double r599895 = z;
        double r599896 = r599895 * r599893;
        double r599897 = r599894 - r599896;
        double r599898 = t;
        double r599899 = r599897 * r599898;
        return r599899;
}
↓
double f(double x, double y, double z, double t) {
        double r599900 = x;
        double r599901 = y;
        double r599902 = r599900 * r599901;
        double r599903 = z;
        double r599904 = r599903 * r599901;
        double r599905 = r599902 - r599904;
        double r599906 = -6.500345540636497e+272;
        bool r599907 = r599905 <= r599906;
        double r599908 = 6.666277602291782e+272;
        bool r599909 = r599905 <= r599908;
        double r599910 = !r599909;
        bool r599911 = r599907 || r599910;
        double r599912 = r599900 - r599903;
        double r599913 = t;
        double r599914 = r599912 * r599913;
        double r599915 = r599901 * r599914;
        double r599916 = r599905 * r599913;
        double r599917 = r599911 ? r599915 : r599916;
        return r599917;
}

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

Original6.7
Target2.8
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -6.500345540636497e+272 or 6.666277602291782e+272 < (- (* x y) (* z y))

    1. Initial program 46.3

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

    3. Applied distribute-rgt-out--46.3

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

    4. Applied associate-*l*0.3

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

    if -6.500345540636497e+272 < (- (* x y) (* z y)) < 6.666277602291782e+272

    1. Initial program 1.5

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -6.5003455406364965 \cdot 10^{272} \lor \neg \left(x \cdot y - z \cdot y \le 6.6662776022917816 \cdot 10^{272}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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))