Average Error: 6.8 → 2.6
Time: 9.4s
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 r543675 = x;
        double r543676 = y;
        double r543677 = r543675 * r543676;
        double r543678 = z;
        double r543679 = r543678 * r543676;
        double r543680 = r543677 - r543679;
        double r543681 = t;
        double r543682 = r543680 * r543681;
        return r543682;
}
↓
double f(double x, double y, double z, double t) {
        double r543683 = t;
        double r543684 = -6.615416921974751e-26;
        bool r543685 = r543683 <= r543684;
        double r543686 = 752007501190631.0;
        bool r543687 = r543683 <= r543686;
        double r543688 = !r543687;
        bool r543689 = r543685 || r543688;
        double r543690 = y;
        double r543691 = x;
        double r543692 = z;
        double r543693 = r543691 - r543692;
        double r543694 = r543690 * r543693;
        double r543695 = r543694 * r543683;
        double r543696 = r543693 * r543683;
        double r543697 = r543690 * r543696;
        double r543698 = r543689 ? r543695 : r543697;
        return r543698;
}

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))