Average Error: 6.7 → 1.5
Time: 14.7s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -3.3572243601805693 \cdot 10^{-45}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -0.0:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;\left(x \cdot y - z \cdot y\right) \cdot t \le 3.6377079460646548 \cdot 10^{+283}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array}\]
\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(x - z\right) \cdot \left(t \cdot y\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r28869789 = x;
        double r28869790 = y;
        double r28869791 = r28869789 * r28869790;
        double r28869792 = z;
        double r28869793 = r28869792 * r28869790;
        double r28869794 = r28869791 - r28869793;
        double r28869795 = t;
        double r28869796 = r28869794 * r28869795;
        return r28869796;
}
↓
double f(double x, double y, double z, double t) {
        double r28869797 = x;
        double r28869798 = y;
        double r28869799 = r28869797 * r28869798;
        double r28869800 = z;
        double r28869801 = r28869800 * r28869798;
        double r28869802 = r28869799 - r28869801;
        double r28869803 = t;
        double r28869804 = r28869802 * r28869803;
        double r28869805 = -3.3572243601805693e-45;
        bool r28869806 = r28869804 <= r28869805;
        double r28869807 = r28869797 - r28869800;
        double r28869808 = r28869803 * r28869798;
        double r28869809 = r28869807 * r28869808;
        double r28869810 = -0.0;
        bool r28869811 = r28869804 <= r28869810;
        double r28869812 = r28869807 * r28869803;
        double r28869813 = r28869812 * r28869798;
        double r28869814 = 3.6377079460646548e+283;
        bool r28869815 = r28869804 <= r28869814;
        double r28869816 = r28869815 ? r28869804 : r28869809;
        double r28869817 = r28869811 ? r28869813 : r28869816;
        double r28869818 = r28869806 ? r28869809 : r28869817;
        return r28869818;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 15.7

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

    2. Simplified2.1

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

    if -3.3572243601805693e-45 < (* (- (* x y) (* z y)) t) < -0.0

    1. Initial program 4.5

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

    2. Simplified9.9

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

    4. Applied associate-*r*2.5

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

    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 simplification1.5

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

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))