Average Error: 6.7 → 1.7
Time: 13.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -3.3572243601805693 \cdot 10^{-45}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -0.0:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le 3.6377079460646548 \cdot 10^{+283}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -3.3572243601805693 \cdot 10^{-45}:\\
\;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\

\mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -0.0:\\
\;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\

\mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le 3.6377079460646548 \cdot 10^{+283}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r12121913 = x;
        double r12121914 = y;
        double r12121915 = r12121913 * r12121914;
        double r12121916 = z;
        double r12121917 = r12121916 * r12121914;
        double r12121918 = r12121915 - r12121917;
        double r12121919 = t;
        double r12121920 = r12121918 * r12121919;
        return r12121920;
}
↓
double f(double x, double y, double z, double t) {
        double r12121921 = x;
        double r12121922 = y;
        double r12121923 = r12121921 * r12121922;
        double r12121924 = z;
        double r12121925 = r12121924 * r12121922;
        double r12121926 = r12121923 - r12121925;
        double r12121927 = t;
        double r12121928 = r12121926 * r12121927;
        double r12121929 = -3.3572243601805693e-45;
        bool r12121930 = r12121928 <= r12121929;
        double r12121931 = r12121921 - r12121924;
        double r12121932 = r12121927 * r12121922;
        double r12121933 = r12121931 * r12121932;
        double r12121934 = -0.0;
        bool r12121935 = r12121928 <= r12121934;
        double r12121936 = r12121931 * r12121927;
        double r12121937 = r12121936 * r12121922;
        double r12121938 = 3.6377079460646548e+283;
        bool r12121939 = r12121928 <= r12121938;
        double r12121940 = r12121939 ? r12121928 : r12121937;
        double r12121941 = r12121935 ? r12121937 : r12121940;
        double r12121942 = r12121930 ? r12121933 : r12121941;
        return r12121942;
}

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
Target3.0
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- (* x y) (* z y)) t) < -3.3572243601805693e-45

    1. Initial program 8.9

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

    2. Simplified2.0

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

    if -3.3572243601805693e-45 < (* (- (* x y) (* z y)) t) < -0.0 or 3.6377079460646548e+283 < (* (- (* x y) (* z y)) t)

    1. Initial program 12.3

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

    2. Simplified8.5

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

    4. Applied associate-*r*3.0

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

    if -0.0 < (* (- (* x y) (* z y)) t) < 3.6377079460646548e+283

    1. Initial program 0.4

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -3.3572243601805693 \cdot 10^{-45}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -0.0:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le 3.6377079460646548 \cdot 10^{+283}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +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))