Average Error: 7.1 → 2.8
Time: 3.3s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -342722408881815676658728613157965559496700 \lor \neg \left(y \le 38654863710312.2421875\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 \cdot \left(y \cdot \left(x - z\right)\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -342722408881815676658728613157965559496700 \lor \neg \left(y \le 38654863710312.2421875\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(1 \cdot \left(y \cdot \left(x - z\right)\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r525970 = x;
        double r525971 = y;
        double r525972 = r525970 * r525971;
        double r525973 = z;
        double r525974 = r525973 * r525971;
        double r525975 = r525972 - r525974;
        double r525976 = t;
        double r525977 = r525975 * r525976;
        return r525977;
}
↓
double f(double x, double y, double z, double t) {
        double r525978 = y;
        double r525979 = -3.4272240888181568e+41;
        bool r525980 = r525978 <= r525979;
        double r525981 = 38654863710312.24;
        bool r525982 = r525978 <= r525981;
        double r525983 = !r525982;
        bool r525984 = r525980 || r525983;
        double r525985 = t;
        double r525986 = r525985 * r525978;
        double r525987 = x;
        double r525988 = z;
        double r525989 = r525987 - r525988;
        double r525990 = r525986 * r525989;
        double r525991 = 1.0;
        double r525992 = r525978 * r525989;
        double r525993 = r525991 * r525992;
        double r525994 = r525985 * r525993;
        double r525995 = r525984 ? r525990 : r525994;
        return r525995;
}

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

Original7.1
Target3.0
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.4272240888181568e+41 or 38654863710312.24 < y

    1. Initial program 16.6

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

    2. Simplified16.6

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

    4. Applied associate-*r*4.0

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

    if -3.4272240888181568e+41 < y < 38654863710312.24

    1. Initial program 2.1

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

    2. Simplified2.1

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

    4. Applied *-un-lft-identity2.1

      \[\leadsto t \cdot \color{blue}{\left(1 \cdot \left(y \cdot \left(x - z\right)\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -342722408881815676658728613157965559496700 \lor \neg \left(y \le 38654863710312.2421875\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 \cdot \left(y \cdot \left(x - z\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))