Average Error: 6.9 → 1.5
Time: 5.7s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.6668607362608217 \cdot 10^{+276} \lor \neg \left(x \cdot y - y \cdot z \leq 2.1225363918014765 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -2.6668607362608217 \cdot 10^{+276} \lor \neg \left(x \cdot y - y \cdot z \leq 2.1225363918014765 \cdot 10^{+204}\right):\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\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) (y * z)))) <= -2.6668607362608217e+276) || !(((double) (((double) (x * y)) - ((double) (y * z)))) <= 2.1225363918014765e+204))) {
		VAR = ((double) (y * ((double) (t * ((double) (x - z))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * 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

Original6.9
Target3.4
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -2.6668607362608217e276 or 2.1225363918014765e204 < (- (* x y) (* z y))

    1. Initial program Error: 35.4 bits

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

    2. SimplifiedError: 0.8 bits

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

    if -2.6668607362608217e276 < (- (* x y) (* z y)) < 2.1225363918014765e204

    1. Initial program Error: 1.6 bits

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

  4. Final simplificationError: 1.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.6668607362608217 \cdot 10^{+276} \lor \neg \left(x \cdot y - y \cdot z \leq 2.1225363918014765 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))