Average Error: 7.5 → 2.2
Time: 3.5s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\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 r537183 = x;
        double r537184 = y;
        double r537185 = r537183 * r537184;
        double r537186 = z;
        double r537187 = r537186 * r537184;
        double r537188 = r537185 - r537187;
        double r537189 = t;
        double r537190 = r537188 * r537189;
        return r537190;
}
↓
double f(double x, double y, double z, double t) {
        double r537191 = x;
        double r537192 = y;
        double r537193 = r537191 * r537192;
        double r537194 = z;
        double r537195 = r537194 * r537192;
        double r537196 = r537193 - r537195;
        double r537197 = -1.8183640740776212e+283;
        bool r537198 = r537196 <= r537197;
        double r537199 = t;
        double r537200 = r537192 * r537199;
        double r537201 = r537191 - r537194;
        double r537202 = r537200 * r537201;
        double r537203 = 2.592867859186123e+96;
        bool r537204 = r537196 <= r537203;
        double r537205 = r537196 * r537199;
        double r537206 = r537201 * r537199;
        double r537207 = r537192 * r537206;
        double r537208 = r537204 ? r537205 : r537207;
        double r537209 = r537198 ? r537202 : r537208;
        return r537209;
}

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

Original7.5
Target3.2
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -1.8183640740776212e+283

    1. Initial program 52.5

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

    3. Applied distribute-rgt-out--52.5

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

    4. Applied associate-*l*0.3

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

    6. Applied add-cube-cbrt1.5

      \[\leadsto y \cdot \left(\left(x - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right)\]

    7. Applied associate-*r*1.5

      \[\leadsto y \cdot \color{blue}{\left(\left(\left(x - z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}\right)}\]

    8. Taylor expanded around inf 52.5

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

    9. Simplified0.2

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

    if -1.8183640740776212e+283 < (- (* x y) (* z y)) < 2.592867859186123e+96

    1. Initial program 1.9

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

    if 2.592867859186123e+96 < (- (* x y) (* z y))

    1. Initial program 17.0

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

    3. Applied distribute-rgt-out--17.0

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

    4. Applied associate-*l*4.1

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.8183640740776212 \cdot 10^{283}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 2.59286785918612292 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))