Average Error: 7.1 → 0.4
Time: 18.3s
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 r23784713 = x;
        double r23784714 = y;
        double r23784715 = r23784713 * r23784714;
        double r23784716 = z;
        double r23784717 = r23784716 * r23784714;
        double r23784718 = r23784715 - r23784717;
        double r23784719 = t;
        double r23784720 = r23784718 * r23784719;
        return r23784720;
}
↓
double f(double x, double y, double z, double t) {
        double r23784721 = x;
        double r23784722 = y;
        double r23784723 = r23784721 * r23784722;
        double r23784724 = z;
        double r23784725 = r23784724 * r23784722;
        double r23784726 = r23784723 - r23784725;
        double r23784727 = -5.992720354667755e+220;
        bool r23784728 = r23784726 <= r23784727;
        double r23784729 = r23784721 - r23784724;
        double r23784730 = t;
        double r23784731 = r23784722 * r23784730;
        double r23784732 = r23784729 * r23784731;
        double r23784733 = -2.396235895919903e-261;
        bool r23784734 = r23784726 <= r23784733;
        double r23784735 = r23784730 * r23784726;
        double r23784736 = 2.2345883147309337e-234;
        bool r23784737 = r23784726 <= r23784736;
        double r23784738 = 4.3197616206806685e+234;
        bool r23784739 = r23784726 <= r23784738;
        double r23784740 = r23784730 * r23784729;
        double r23784741 = r23784740 * r23784722;
        double r23784742 = r23784739 ? r23784735 : r23784741;
        double r23784743 = r23784737 ? r23784732 : r23784742;
        double r23784744 = r23784734 ? r23784735 : r23784743;
        double r23784745 = r23784728 ? r23784732 : r23784744;
        return r23784745;
}

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 +o rules:numerics
(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))