Average Error: 7.2 → 1.4
Time: 4.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -9.0146955933035551 \cdot 10^{293} \lor \neg \left(x \cdot y - z \cdot y \le 1.5582855698097887 \cdot 10^{247}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -9.0146955933035551 \cdot 10^{293} \lor \neg \left(x \cdot y - z \cdot y \le 1.5582855698097887 \cdot 10^{247}\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 r446078 = x;
        double r446079 = y;
        double r446080 = r446078 * r446079;
        double r446081 = z;
        double r446082 = r446081 * r446079;
        double r446083 = r446080 - r446082;
        double r446084 = t;
        double r446085 = r446083 * r446084;
        return r446085;
}
↓
double f(double x, double y, double z, double t) {
        double r446086 = x;
        double r446087 = y;
        double r446088 = r446086 * r446087;
        double r446089 = z;
        double r446090 = r446089 * r446087;
        double r446091 = r446088 - r446090;
        double r446092 = -9.014695593303555e+293;
        bool r446093 = r446091 <= r446092;
        double r446094 = 1.5582855698097887e+247;
        bool r446095 = r446091 <= r446094;
        double r446096 = !r446095;
        bool r446097 = r446093 || r446096;
        double r446098 = r446086 - r446089;
        double r446099 = t;
        double r446100 = r446098 * r446099;
        double r446101 = r446087 * r446100;
        double r446102 = r446091 * r446099;
        double r446103 = r446097 ? r446101 : r446102;
        return r446103;
}

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

Original7.2
Target3.1
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -9.014695593303555e+293 or 1.5582855698097887e+247 < (- (* x y) (* z y))

    1. Initial program 46.4

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

    3. Applied distribute-rgt-out--46.4

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

    4. Applied associate-*l*0.5

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

    if -9.014695593303555e+293 < (- (* x y) (* z y)) < 1.5582855698097887e+247

    1. Initial program 1.6

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -9.0146955933035551 \cdot 10^{293} \lor \neg \left(x \cdot y - z \cdot y \le 1.5582855698097887 \cdot 10^{247}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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))