Average Error: 7.4 → 0.5
Time: 10.9s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -9.28546639189079822726342632154485811791 \cdot 10^{-250} \lor \neg \left(x \cdot y - z \cdot y \le 1.207146899072114501620361812179724065154 \cdot 10^{-243}\right) \land x \cdot y - z \cdot y \le 9.010117805898266714360417458543683393234 \cdot 10^{141}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\
\;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -9.28546639189079822726342632154485811791 \cdot 10^{-250} \lor \neg \left(x \cdot y - z \cdot y \le 1.207146899072114501620361812179724065154 \cdot 10^{-243}\right) \land x \cdot y - z \cdot y \le 9.010117805898266714360417458543683393234 \cdot 10^{141}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r332278 = x;
        double r332279 = y;
        double r332280 = r332278 * r332279;
        double r332281 = z;
        double r332282 = r332281 * r332279;
        double r332283 = r332280 - r332282;
        double r332284 = t;
        double r332285 = r332283 * r332284;
        return r332285;
}
↓
double f(double x, double y, double z, double t) {
        double r332286 = x;
        double r332287 = y;
        double r332288 = r332286 * r332287;
        double r332289 = z;
        double r332290 = r332289 * r332287;
        double r332291 = r332288 - r332290;
        double r332292 = -inf.0;
        bool r332293 = r332291 <= r332292;
        double r332294 = t;
        double r332295 = r332286 - r332289;
        double r332296 = r332294 * r332295;
        double r332297 = r332296 * r332287;
        double r332298 = -9.285466391890798e-250;
        bool r332299 = r332291 <= r332298;
        double r332300 = 1.2071468990721145e-243;
        bool r332301 = r332291 <= r332300;
        double r332302 = !r332301;
        double r332303 = 9.010117805898267e+141;
        bool r332304 = r332291 <= r332303;
        bool r332305 = r332302 && r332304;
        bool r332306 = r332299 || r332305;
        double r332307 = r332294 * r332291;
        double r332308 = r332287 * r332294;
        double r332309 = r332295 * r332308;
        double r332310 = r332306 ? r332307 : r332309;
        double r332311 = r332293 ? r332297 : r332310;
        return r332311;
}

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

Original7.4
Target3.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -inf.0

    1. Initial program 64.0

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

    2. Simplified0.3

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

    4. Applied associate-*r*0.2

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

    if -inf.0 < (- (* x y) (* z y)) < -9.285466391890798e-250 or 1.2071468990721145e-243 < (- (* x y) (* z y)) < 9.010117805898267e+141

    1. Initial program 0.2

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

    if -9.285466391890798e-250 < (- (* x y) (* z y)) < 1.2071468990721145e-243 or 9.010117805898267e+141 < (- (* x y) (* z y))

    1. Initial program 18.2

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

    2. Simplified1.2

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -9.28546639189079822726342632154485811791 \cdot 10^{-250} \lor \neg \left(x \cdot y - z \cdot y \le 1.207146899072114501620361812179724065154 \cdot 10^{-243}\right) \land x \cdot y - z \cdot y \le 9.010117805898266714360417458543683393234 \cdot 10^{141}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"

  :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))