Average Error: 7.1 → 0.7
Time: 3.3s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.28824894235068545 \cdot 10^{303} \lor \neg \left(x \cdot y - z \cdot y \le -4.7564680486971018 \cdot 10^{-95} \lor \neg \left(x \cdot y - z \cdot y \le 6.6450334734924226 \cdot 10^{-297} \lor \neg \left(x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -4.28824894235068545 \cdot 10^{303} \lor \neg \left(x \cdot y - z \cdot y \le -4.7564680486971018 \cdot 10^{-95} \lor \neg \left(x \cdot y - z \cdot y \le 6.6450334734924226 \cdot 10^{-297} \lor \neg \left(x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\right)\right)\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 r554898 = x;
        double r554899 = y;
        double r554900 = r554898 * r554899;
        double r554901 = z;
        double r554902 = r554901 * r554899;
        double r554903 = r554900 - r554902;
        double r554904 = t;
        double r554905 = r554903 * r554904;
        return r554905;
}
↓
double f(double x, double y, double z, double t) {
        double r554906 = x;
        double r554907 = y;
        double r554908 = r554906 * r554907;
        double r554909 = z;
        double r554910 = r554909 * r554907;
        double r554911 = r554908 - r554910;
        double r554912 = -4.2882489423506854e+303;
        bool r554913 = r554911 <= r554912;
        double r554914 = -4.756468048697102e-95;
        bool r554915 = r554911 <= r554914;
        double r554916 = 6.645033473492423e-297;
        bool r554917 = r554911 <= r554916;
        double r554918 = 6.615880882346356e+208;
        bool r554919 = r554911 <= r554918;
        double r554920 = !r554919;
        bool r554921 = r554917 || r554920;
        double r554922 = !r554921;
        bool r554923 = r554915 || r554922;
        double r554924 = !r554923;
        bool r554925 = r554913 || r554924;
        double r554926 = r554906 - r554909;
        double r554927 = t;
        double r554928 = r554926 * r554927;
        double r554929 = r554907 * r554928;
        double r554930 = r554911 * r554927;
        double r554931 = r554925 ? r554929 : r554930;
        return r554931;
}

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

Original7.1
Target3.1
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -4.2882489423506854e+303 or -4.756468048697102e-95 < (- (* x y) (* z y)) < 6.645033473492423e-297 or 6.615880882346356e+208 < (- (* x y) (* z y))

    1. Initial program 22.6

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

    3. Applied distribute-rgt-out--22.6

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

    4. Applied associate-*l*1.7

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

    if -4.2882489423506854e+303 < (- (* x y) (* z y)) < -4.756468048697102e-95 or 6.645033473492423e-297 < (- (* x y) (* z y)) < 6.615880882346356e+208

    1. Initial program 0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.28824894235068545 \cdot 10^{303} \lor \neg \left(x \cdot y - z \cdot y \le -4.7564680486971018 \cdot 10^{-95} \lor \neg \left(x \cdot y - z \cdot y \le 6.6450334734924226 \cdot 10^{-297} \lor \neg \left(x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))