Average Error: 7.0 → 1.5
Time: 3.5s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.96419464480742733 \cdot 10^{292} \lor \neg \left(x \cdot y - z \cdot y \le 2.9445630519759346 \cdot 10^{215}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -1.96419464480742733 \cdot 10^{292} \lor \neg \left(x \cdot y - z \cdot y \le 2.9445630519759346 \cdot 10^{215}\right):\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r571160 = x;
        double r571161 = y;
        double r571162 = r571160 * r571161;
        double r571163 = z;
        double r571164 = r571163 * r571161;
        double r571165 = r571162 - r571164;
        double r571166 = t;
        double r571167 = r571165 * r571166;
        return r571167;
}
↓
double f(double x, double y, double z, double t) {
        double r571168 = x;
        double r571169 = y;
        double r571170 = r571168 * r571169;
        double r571171 = z;
        double r571172 = r571171 * r571169;
        double r571173 = r571170 - r571172;
        double r571174 = -1.9641946448074273e+292;
        bool r571175 = r571173 <= r571174;
        double r571176 = 2.9445630519759346e+215;
        bool r571177 = r571173 <= r571176;
        double r571178 = !r571177;
        bool r571179 = r571175 || r571178;
        double r571180 = r571168 - r571171;
        double r571181 = t;
        double r571182 = r571180 * r571181;
        double r571183 = r571169 * r571182;
        double r571184 = r571173 * r571181;
        double r571185 = r571179 ? r571183 : r571184;
        return r571185;
}

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

Original7.0
Target3.0
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -1.9641946448074273e+292 or 2.9445630519759346e+215 < (- (* x y) (* z y))

    1. Initial program 39.4

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

    3. Applied distribute-rgt-out--39.4

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

    4. Applied associate-*l*0.7

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

    if -1.9641946448074273e+292 < (- (* x y) (* z y)) < 2.9445630519759346e+215

    1. Initial program 1.6

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.96419464480742733 \cdot 10^{292} \lor \neg \left(x \cdot y - z \cdot y \le 2.9445630519759346 \cdot 10^{215}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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))