Average Error: 6.8 → 2.6
Time: 10.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.6154169219747513 \cdot 10^{-26} \lor \neg \left(t \le 752007501190631\right):\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le -6.6154169219747513 \cdot 10^{-26} \lor \neg \left(t \le 752007501190631\right):\\
\;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r645834 = x;
        double r645835 = y;
        double r645836 = r645834 * r645835;
        double r645837 = z;
        double r645838 = r645837 * r645835;
        double r645839 = r645836 - r645838;
        double r645840 = t;
        double r645841 = r645839 * r645840;
        return r645841;
}
↓
double f(double x, double y, double z, double t) {
        double r645842 = t;
        double r645843 = -6.615416921974751e-26;
        bool r645844 = r645842 <= r645843;
        double r645845 = 752007501190631.0;
        bool r645846 = r645842 <= r645845;
        double r645847 = !r645846;
        bool r645848 = r645844 || r645847;
        double r645849 = y;
        double r645850 = x;
        double r645851 = z;
        double r645852 = r645850 - r645851;
        double r645853 = r645849 * r645852;
        double r645854 = r645853 * r645842;
        double r645855 = r645852 * r645842;
        double r645856 = r645849 * r645855;
        double r645857 = r645848 ? r645854 : r645856;
        return r645857;
}

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

Original6.8
Target3.0
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -6.615416921974751e-26 or 752007501190631.0 < t

    1. Initial program 3.3

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--3.3

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

    4. Applied associate-*l*14.6

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

    6. Applied associate-*r*3.3

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

    if -6.615416921974751e-26 < t < 752007501190631.0

    1. Initial program 9.1

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--9.1

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

    4. Applied associate-*l*2.1

      \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.6154169219747513 \cdot 10^{-26} \lor \neg \left(t \le 752007501190631\right):\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :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))