Average Error: 7.3 → 7.1
Time: 4.5s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.20924086246930474 \cdot 10^{-120} \lor \neg \left(t \le -3.1972000332428539 \cdot 10^{-226} \lor \neg \left(t \le 4.78914985574116521 \cdot 10^{-286} \lor \neg \left(t \le 4.146211365397844 \cdot 10^{222}\right)\right)\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.20924086246930474 \cdot 10^{-120} \lor \neg \left(t \le -3.1972000332428539 \cdot 10^{-226} \lor \neg \left(t \le 4.78914985574116521 \cdot 10^{-286} \lor \neg \left(t \le 4.146211365397844 \cdot 10^{222}\right)\right)\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((t <= -1.2092408624693047e-120) || !((t <= -3.197200033242854e-226) || !((t <= 4.789149855741165e-286) || !(t <= 4.146211365397844e+222))))) {
		VAR = ((double) (((double) (t * y)) * ((double) (x - z))));
	} else {
		VAR = ((double) (t * ((double) (y * ((double) (x - z))))));
	}
	return VAR;
}

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

Original7.3
Target3.1
Herbie7.1
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.2092408624693047e-120 or -3.197200033242854e-226 < t < 4.789149855741165e-286 or 4.146211365397844e+222 < t

    1. Initial program 6.9

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Simplified6.9

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(x - z\right)\right)}\]
    3. Using strategy rm

    4. Applied associate-*r*6.4

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

    if -1.2092408624693047e-120 < t < -3.197200033242854e-226 or 4.789149855741165e-286 < t < 4.146211365397844e+222

    1. Initial program 7.7

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Simplified7.7

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

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.20924086246930474 \cdot 10^{-120} \lor \neg \left(t \le -3.1972000332428539 \cdot 10^{-226} \lor \neg \left(t \le 4.78914985574116521 \cdot 10^{-286} \lor \neg \left(t \le 4.146211365397844 \cdot 10^{222}\right)\right)\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020129 
(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))