Average Error: 7.1 → 0.4
Time: 17.5s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -5.992720354667754811931564301530949164485 \cdot 10^{220}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -2.396235895919902913371156822147246977413 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.234588314730933664591068695313985424095 \cdot 10^{-234}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 4.319761620680668531396215097486412798471 \cdot 10^{234}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -5.992720354667754811931564301530949164485 \cdot 10^{220}:\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -2.396235895919902913371156822147246977413 \cdot 10^{-261}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 2.234588314730933664591068695313985424095 \cdot 10^{-234}:\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 4.319761620680668531396215097486412798471 \cdot 10^{234}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r29005851 = x;
        double r29005852 = y;
        double r29005853 = r29005851 * r29005852;
        double r29005854 = z;
        double r29005855 = r29005854 * r29005852;
        double r29005856 = r29005853 - r29005855;
        double r29005857 = t;
        double r29005858 = r29005856 * r29005857;
        return r29005858;
}
↓
double f(double x, double y, double z, double t) {
        double r29005859 = x;
        double r29005860 = y;
        double r29005861 = r29005859 * r29005860;
        double r29005862 = z;
        double r29005863 = r29005862 * r29005860;
        double r29005864 = r29005861 - r29005863;
        double r29005865 = -5.992720354667755e+220;
        bool r29005866 = r29005864 <= r29005865;
        double r29005867 = r29005859 - r29005862;
        double r29005868 = t;
        double r29005869 = r29005860 * r29005868;
        double r29005870 = r29005867 * r29005869;
        double r29005871 = -2.396235895919903e-261;
        bool r29005872 = r29005864 <= r29005871;
        double r29005873 = r29005868 * r29005864;
        double r29005874 = 2.2345883147309337e-234;
        bool r29005875 = r29005864 <= r29005874;
        double r29005876 = 4.3197616206806685e+234;
        bool r29005877 = r29005864 <= r29005876;
        double r29005878 = r29005868 * r29005867;
        double r29005879 = r29005878 * r29005860;
        double r29005880 = r29005877 ? r29005873 : r29005879;
        double r29005881 = r29005875 ? r29005870 : r29005880;
        double r29005882 = r29005872 ? r29005873 : r29005881;
        double r29005883 = r29005866 ? r29005870 : r29005882;
        return r29005883;
}

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
Target2.9
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -5.992720354667755e+220 or -2.396235895919903e-261 < (- (* x y) (* z y)) < 2.2345883147309337e-234

    1. Initial program 21.4

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

    2. Simplified0.6

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

    if -5.992720354667755e+220 < (- (* x y) (* z y)) < -2.396235895919903e-261 or 2.2345883147309337e-234 < (- (* x y) (* z y)) < 4.3197616206806685e+234

    1. Initial program 0.2

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

    if 4.3197616206806685e+234 < (- (* x y) (* z y))

    1. Initial program 38.5

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

    2. Simplified0.5

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

    4. Applied associate-*r*0.9

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -5.992720354667754811931564301530949164485 \cdot 10^{220}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -2.396235895919902913371156822147246977413 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.234588314730933664591068695313985424095 \cdot 10^{-234}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 4.319761620680668531396215097486412798471 \cdot 10^{234}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"

  :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))