Average Error: 7.1 → 0.7
Time: 8.4s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.28824894235068545 \cdot 10^{303} \lor \neg \left(x \cdot y - z \cdot y \le -4.7564680486971018 \cdot 10^{-95} \lor \neg \left(x \cdot y - z \cdot y \le 6.6450334734924226 \cdot 10^{-297}\right) \land x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\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}\right) \land x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\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 r1178161 = x;
        double r1178162 = y;
        double r1178163 = r1178161 * r1178162;
        double r1178164 = z;
        double r1178165 = r1178164 * r1178162;
        double r1178166 = r1178163 - r1178165;
        double r1178167 = t;
        double r1178168 = r1178166 * r1178167;
        return r1178168;
}
↓
double f(double x, double y, double z, double t) {
        double r1178169 = x;
        double r1178170 = y;
        double r1178171 = r1178169 * r1178170;
        double r1178172 = z;
        double r1178173 = r1178172 * r1178170;
        double r1178174 = r1178171 - r1178173;
        double r1178175 = -4.2882489423506854e+303;
        bool r1178176 = r1178174 <= r1178175;
        double r1178177 = -4.756468048697102e-95;
        bool r1178178 = r1178174 <= r1178177;
        double r1178179 = 6.645033473492423e-297;
        bool r1178180 = r1178174 <= r1178179;
        double r1178181 = !r1178180;
        double r1178182 = 6.615880882346356e+208;
        bool r1178183 = r1178174 <= r1178182;
        bool r1178184 = r1178181 && r1178183;
        bool r1178185 = r1178178 || r1178184;
        double r1178186 = !r1178185;
        bool r1178187 = r1178176 || r1178186;
        double r1178188 = r1178169 - r1178172;
        double r1178189 = t;
        double r1178190 = r1178188 * r1178189;
        double r1178191 = r1178170 * r1178190;
        double r1178192 = r1178174 * r1178189;
        double r1178193 = r1178187 ? r1178191 : r1178192;
        return r1178193;
}

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

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

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))