Average Error: 7.4 → 0.5
Time: 12.4s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -9.28546639189079822726342632154485811791 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.207146899072114501620361812179724065154 \cdot 10^{-243}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 9.010117805898266714360417458543683393234 \cdot 10^{141}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]
\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}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.207146899072114501620361812179724065154 \cdot 10^{-243}:\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

\mathbf{elif}\;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 r20887821 = x;
        double r20887822 = y;
        double r20887823 = r20887821 * r20887822;
        double r20887824 = z;
        double r20887825 = r20887824 * r20887822;
        double r20887826 = r20887823 - r20887825;
        double r20887827 = t;
        double r20887828 = r20887826 * r20887827;
        return r20887828;
}
↓
double f(double x, double y, double z, double t) {
        double r20887829 = x;
        double r20887830 = y;
        double r20887831 = r20887829 * r20887830;
        double r20887832 = z;
        double r20887833 = r20887832 * r20887830;
        double r20887834 = r20887831 - r20887833;
        double r20887835 = -inf.0;
        bool r20887836 = r20887834 <= r20887835;
        double r20887837 = t;
        double r20887838 = r20887829 - r20887832;
        double r20887839 = r20887837 * r20887838;
        double r20887840 = r20887839 * r20887830;
        double r20887841 = -9.285466391890798e-250;
        bool r20887842 = r20887834 <= r20887841;
        double r20887843 = r20887837 * r20887834;
        double r20887844 = 1.2071468990721145e-243;
        bool r20887845 = r20887834 <= r20887844;
        double r20887846 = r20887830 * r20887837;
        double r20887847 = r20887838 * r20887846;
        double r20887848 = 9.010117805898267e+141;
        bool r20887849 = r20887834 <= r20887848;
        double r20887850 = r20887849 ? r20887843 : r20887847;
        double r20887851 = r20887845 ? r20887847 : r20887850;
        double r20887852 = r20887842 ? r20887843 : r20887851;
        double r20887853 = r20887836 ? r20887840 : r20887852;
        return r20887853;
}

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

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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))