Average Error: 7.2 → 0.5
Time: 2.1s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.02275575380614783 \cdot 10^{199}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -6.5915768717592157 \cdot 10^{-274}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 5.5274967453050168 \cdot 10^{-235}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.8505967398661828 \cdot 10^{164}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -1.02275575380614783 \cdot 10^{199}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -6.5915768717592157 \cdot 10^{-274}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 5.5274967453050168 \cdot 10^{-235}:\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.8505967398661828 \cdot 10^{164}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (((x * y) - (z * y)) * t);
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((x * y) - (z * y)) <= -1.0227557538061478e+199)) {
		VAR = (y * (t * (x - z)));
	} else {
		double VAR_1;
		if ((((x * y) - (z * y)) <= -6.591576871759216e-274)) {
			VAR_1 = (((x * y) - (z * y)) * t);
		} else {
			double VAR_2;
			if ((((x * y) - (z * y)) <= 5.527496745305017e-235)) {
				VAR_2 = ((t * y) * (x - z));
			} else {
				double VAR_3;
				if ((((x * y) - (z * y)) <= 1.8505967398661828e+164)) {
					VAR_3 = (((x * y) - (z * y)) * t);
				} else {
					VAR_3 = (y * (t * (x - z)));
				}
				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

Original7.2
Target3.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -1.0227557538061478e+199 or 1.8505967398661828e+164 < (- (* x y) (* z y))

    1. Initial program 25.7

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

    2. Taylor expanded around inf 25.7

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

    3. Simplified1.6

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

    5. Applied *-commutative1.6

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

    6. Applied associate-*l*1.4

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

    if -1.0227557538061478e+199 < (- (* x y) (* z y)) < -6.591576871759216e-274 or 5.527496745305017e-235 < (- (* x y) (* z y)) < 1.8505967398661828e+164

    1. Initial program 0.3

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

    if -6.591576871759216e-274 < (- (* x y) (* z y)) < 5.527496745305017e-235

    1. Initial program 12.6

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

    2. Taylor expanded around inf 12.6

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

    3. Simplified0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -1.02275575380614783 \cdot 10^{199}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -6.5915768717592157 \cdot 10^{-274}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 5.5274967453050168 \cdot 10^{-235}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.8505967398661828 \cdot 10^{164}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(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))