Average Error: 7.1 → 0.7
Time: 10.3s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.28824894235068545 \cdot 10^{303} \lor \neg \left(x \cdot y - z \cdot y \le -4.7564680486971018 \cdot 10^{-95} \lor \neg \left(x \cdot y - z \cdot y \le 6.6450334734924226 \cdot 10^{-297}\right) \land x \cdot y - z \cdot y \le 6.61588088234635616 \cdot 10^{208}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\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 r465283 = x;
        double r465284 = y;
        double r465285 = r465283 * r465284;
        double r465286 = z;
        double r465287 = r465286 * r465284;
        double r465288 = r465285 - r465287;
        double r465289 = t;
        double r465290 = r465288 * r465289;
        return r465290;
}
↓
double f(double x, double y, double z, double t) {
        double r465291 = x;
        double r465292 = y;
        double r465293 = r465291 * r465292;
        double r465294 = z;
        double r465295 = r465294 * r465292;
        double r465296 = r465293 - r465295;
        double r465297 = -4.2882489423506854e+303;
        bool r465298 = r465296 <= r465297;
        double r465299 = -4.756468048697102e-95;
        bool r465300 = r465296 <= r465299;
        double r465301 = 6.645033473492423e-297;
        bool r465302 = r465296 <= r465301;
        double r465303 = !r465302;
        double r465304 = 6.615880882346356e+208;
        bool r465305 = r465296 <= r465304;
        bool r465306 = r465303 && r465305;
        bool r465307 = r465300 || r465306;
        double r465308 = !r465307;
        bool r465309 = r465298 || r465308;
        double r465310 = r465291 - r465294;
        double r465311 = t;
        double r465312 = r465310 * r465311;
        double r465313 = r465292 * r465312;
        double r465314 = r465296 * r465311;
        double r465315 = r465309 ? r465313 : r465314;
        return r465315;
}

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 +o rules:numerics
(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))