Average Error: 6.7 → 1.7
Time: 12.0s
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 r26573840 = x;
        double r26573841 = y;
        double r26573842 = r26573840 * r26573841;
        double r26573843 = z;
        double r26573844 = r26573843 * r26573841;
        double r26573845 = r26573842 - r26573844;
        double r26573846 = t;
        double r26573847 = r26573845 * r26573846;
        return r26573847;
}
↓
double f(double x, double y, double z, double t) {
        double r26573848 = x;
        double r26573849 = y;
        double r26573850 = r26573848 * r26573849;
        double r26573851 = z;
        double r26573852 = r26573851 * r26573849;
        double r26573853 = r26573850 - r26573852;
        double r26573854 = t;
        double r26573855 = r26573853 * r26573854;
        double r26573856 = -3.3572243601805693e-45;
        bool r26573857 = r26573855 <= r26573856;
        double r26573858 = r26573848 - r26573851;
        double r26573859 = r26573854 * r26573849;
        double r26573860 = r26573858 * r26573859;
        double r26573861 = -0.0;
        bool r26573862 = r26573855 <= r26573861;
        double r26573863 = r26573858 * r26573854;
        double r26573864 = r26573863 * r26573849;
        double r26573865 = 3.6377079460646548e+283;
        bool r26573866 = r26573855 <= r26573865;
        double r26573867 = r26573866 ? r26573855 : r26573864;
        double r26573868 = r26573862 ? r26573864 : r26573867;
        double r26573869 = r26573857 ? r26573860 : r26573868;
        return r26573869;
}

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 
(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))