Average Error: 7.1 → 0.4
Time: 18.6s
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 r21603618 = x;
        double r21603619 = y;
        double r21603620 = r21603618 * r21603619;
        double r21603621 = z;
        double r21603622 = r21603621 * r21603619;
        double r21603623 = r21603620 - r21603622;
        double r21603624 = t;
        double r21603625 = r21603623 * r21603624;
        return r21603625;
}
↓
double f(double x, double y, double z, double t) {
        double r21603626 = x;
        double r21603627 = y;
        double r21603628 = r21603626 * r21603627;
        double r21603629 = z;
        double r21603630 = r21603629 * r21603627;
        double r21603631 = r21603628 - r21603630;
        double r21603632 = -5.992720354667755e+220;
        bool r21603633 = r21603631 <= r21603632;
        double r21603634 = r21603626 - r21603629;
        double r21603635 = t;
        double r21603636 = r21603627 * r21603635;
        double r21603637 = r21603634 * r21603636;
        double r21603638 = -2.396235895919903e-261;
        bool r21603639 = r21603631 <= r21603638;
        double r21603640 = r21603635 * r21603631;
        double r21603641 = 2.2345883147309337e-234;
        bool r21603642 = r21603631 <= r21603641;
        double r21603643 = 4.3197616206806685e+234;
        bool r21603644 = r21603631 <= r21603643;
        double r21603645 = r21603635 * r21603634;
        double r21603646 = r21603645 * r21603627;
        double r21603647 = r21603644 ? r21603640 : r21603646;
        double r21603648 = r21603642 ? r21603637 : r21603647;
        double r21603649 = r21603639 ? r21603640 : r21603648;
        double r21603650 = r21603633 ? r21603637 : r21603649;
        return r21603650;
}

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))