Average Error: 7.6 → 3.5
Time: 2.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;1 \cdot \left(\left(\left(x - z\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x - z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\
\;\;\;\;1 \cdot \left(\left(\left(x - z\right) \cdot t\right) \cdot y\right)\\

\mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \left(\left(x - z\right) \cdot \left(t \cdot y\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r566593 = x;
        double r566594 = y;
        double r566595 = r566593 * r566594;
        double r566596 = z;
        double r566597 = r566596 * r566594;
        double r566598 = r566595 - r566597;
        double r566599 = t;
        double r566600 = r566598 * r566599;
        return r566600;
}
↓
double f(double x, double y, double z, double t) {
        double r566601 = y;
        double r566602 = -1.434059461590054e-73;
        bool r566603 = r566601 <= r566602;
        double r566604 = 1.0;
        double r566605 = x;
        double r566606 = z;
        double r566607 = r566605 - r566606;
        double r566608 = t;
        double r566609 = r566607 * r566608;
        double r566610 = r566609 * r566601;
        double r566611 = r566604 * r566610;
        double r566612 = 8.822188301346798e-152;
        bool r566613 = r566601 <= r566612;
        double r566614 = r566601 * r566607;
        double r566615 = r566608 * r566614;
        double r566616 = r566608 * r566601;
        double r566617 = r566607 * r566616;
        double r566618 = r566604 * r566617;
        double r566619 = r566613 ? r566615 : r566618;
        double r566620 = r566603 ? r566611 : r566619;
        return r566620;
}

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

Original7.6
Target3.1
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.434059461590054e-73

    1. Initial program 12.4

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

    2. Simplified12.4

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

    4. Applied *-un-lft-identity12.4

      \[\leadsto \color{blue}{\left(1 \cdot t\right)} \cdot \left(y \cdot \left(x - z\right)\right)\]

    5. Applied associate-*l*12.4

      \[\leadsto \color{blue}{1 \cdot \left(t \cdot \left(y \cdot \left(x - z\right)\right)\right)}\]

    6. Simplified3.6

      \[\leadsto 1 \cdot \color{blue}{\left(\left(x - z\right) \cdot \left(t \cdot y\right)\right)}\]
    7. Using strategy rm

    8. Applied associate-*r*3.5

      \[\leadsto 1 \cdot \color{blue}{\left(\left(\left(x - z\right) \cdot t\right) \cdot y\right)}\]

    if -1.434059461590054e-73 < y < 8.822188301346798e-152

    1. Initial program 2.9

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

    2. Simplified2.9

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

    if 8.822188301346798e-152 < y

    1. Initial program 9.7

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

    2. Simplified9.7

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

    4. Applied *-un-lft-identity9.7

      \[\leadsto \color{blue}{\left(1 \cdot t\right)} \cdot \left(y \cdot \left(x - z\right)\right)\]

    5. Applied associate-*l*9.7

      \[\leadsto \color{blue}{1 \cdot \left(t \cdot \left(y \cdot \left(x - z\right)\right)\right)}\]

    6. Simplified4.3

      \[\leadsto 1 \cdot \color{blue}{\left(\left(x - z\right) \cdot \left(t \cdot y\right)\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;1 \cdot \left(\left(\left(x - z\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x - z\right) \cdot \left(t \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))