Average Error: 7.0 → 1.7
Time: 3.0s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.69121708284112 \cdot 10^{192} \lor \neg \left(x \cdot y - z \cdot y \le 1.4833312702121893 \cdot 10^{165}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -2.69121708284112 \cdot 10^{192} \lor \neg \left(x \cdot y - z \cdot y \le 1.4833312702121893 \cdot 10^{165}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

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

\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 (((((double) (((double) (x * y)) - ((double) (z * y)))) <= -2.69121708284112e+192) || !(((double) (((double) (x * y)) - ((double) (z * y)))) <= 1.4833312702121893e+165))) {
		VAR = ((double) (((double) (t * y)) * ((double) (x - z))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
	}
	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

Original7.0
Target3.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -2.69121708284112e+192 or 1.4833312702121893e+165 < (- (* x y) (* z y))

    1. Initial program 24.2

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

    2. Simplified24.2

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

    4. Applied associate-*r*1.5

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

    if -2.69121708284112e+192 < (- (* x y) (* z y)) < 1.4833312702121893e+165

    1. Initial program 1.7

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.69121708284112 \cdot 10^{192} \lor \neg \left(x \cdot y - z \cdot y \le 1.4833312702121893 \cdot 10^{165}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020124 
(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))