Average Error: 6.9 → 3.3
Time: 15.9s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.856164112248959329219151378456217111614 \cdot 10^{-91} \lor \neg \left(y \le 3.025418364347031062019168566536185959801 \cdot 10^{108}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.856164112248959329219151378456217111614 \cdot 10^{-91} \lor \neg \left(y \le 3.025418364347031062019168566536185959801 \cdot 10^{108}\right):\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r418006 = x;
        double r418007 = y;
        double r418008 = r418006 * r418007;
        double r418009 = z;
        double r418010 = r418009 * r418007;
        double r418011 = r418008 - r418010;
        double r418012 = t;
        double r418013 = r418011 * r418012;
        return r418013;
}
↓
double f(double x, double y, double z, double t) {
        double r418014 = y;
        double r418015 = -4.8561641122489593e-91;
        bool r418016 = r418014 <= r418015;
        double r418017 = 3.025418364347031e+108;
        bool r418018 = r418014 <= r418017;
        double r418019 = !r418018;
        bool r418020 = r418016 || r418019;
        double r418021 = x;
        double r418022 = z;
        double r418023 = r418021 - r418022;
        double r418024 = t;
        double r418025 = r418023 * r418024;
        double r418026 = r418014 * r418025;
        double r418027 = r418014 * r418023;
        double r418028 = r418027 * r418024;
        double r418029 = r418020 ? r418026 : r418028;
        return r418029;
}

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

Original6.9
Target3.2
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.8561641122489593e-91 or 3.025418364347031e+108 < y

    1. Initial program 13.6

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

    2. Simplified13.6

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

    4. Applied associate-*l*3.8

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

    if -4.8561641122489593e-91 < y < 3.025418364347031e+108

    1. Initial program 2.9

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

    2. Simplified2.9

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.856164112248959329219151378456217111614 \cdot 10^{-91} \lor \neg \left(y \le 3.025418364347031062019168566536185959801 \cdot 10^{108}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.2318795828867769e-80) (* (* y t) (- x z)) (if (< t 2.5430670515648771e83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))