Average Error: 6.7 → 0.8
Time: 3.4s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -1.5385565349806358 \cdot 10^{-258}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 6.932349535556259 \cdot 10^{-207}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 3.715654409021787 \cdot 10^{+94}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\
\;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -1.5385565349806358 \cdot 10^{-258}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 6.932349535556259 \cdot 10^{-207}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 3.715654409021787 \cdot 10^{+94}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\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 ((((double) (((double) (x * y)) - ((double) (y * z)))) <= ((double) -(((double) INFINITY))))) {
		VAR = ((double) (((double) (y * ((double) (x * t)))) - ((double) (y * ((double) (z * t))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= -1.5385565349806358e-258)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 6.932349535556259e-207)) {
				VAR_2 = ((double) (((double) (y * t)) * ((double) (x - z))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 3.715654409021787e+94)) {
					VAR_3 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
				} else {
					VAR_3 = ((double) (((double) (y * ((double) (x * t)))) - ((double) (y * ((double) (z * t))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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

Original6.7
Target3.0
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -inf.0 or 3.7156544090217868e94 < (- (* x y) (* z y))

    1. Initial program 25.2

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

    2. Simplified2.5

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

    4. Applied sub-neg2.5

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

    5. Applied distribute-lft-in2.5

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

    6. Applied distribute-lft-in2.5

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

    if -inf.0 < (- (* x y) (* z y)) < -1.53855653498063576e-258 or 6.9323495355562593e-207 < (- (* x y) (* z y)) < 3.7156544090217868e94

    1. Initial program 0.2

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

    if -1.53855653498063576e-258 < (- (* x y) (* z y)) < 6.9323495355562593e-207

    1. Initial program 9.3

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

    2. Simplified0.3

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

    4. Applied associate-*r*0.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -1.5385565349806358 \cdot 10^{-258}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 6.932349535556259 \cdot 10^{-207}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 3.715654409021787 \cdot 10^{+94}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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))