Average Error: 7.0 → 0.8
Time: 3.7s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -1.579478125434173 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 4.0591586060962483 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 2.728593090045186 \cdot 10^{+195}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -\infty:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -1.579478125434173 \cdot 10^{-301}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 4.0591586060962483 \cdot 10^{-289}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 2.728593090045186 \cdot 10^{+195}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (* (- (* x y) (* z y)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (* (- (* x y) (* y z)) t) (- INFINITY))
   (* y (* t (- x z)))
   (if (<= (* (- (* x y) (* y z)) t) -1.579478125434173e-301)
     (* (- (* x y) (* y z)) t)
     (if (<= (* (- (* x y) (* y z)) t) 4.0591586060962483e-289)
       (* y (* t (- x z)))
       (if (<= (* (- (* x y) (* y z)) t) 2.728593090045186e+195)
         (* (- (* x y) (* y z)) t)
         (* (- x z) (* y t)))))))
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 tmp;
	if ((((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t)) <= ((double) -(((double) INFINITY))))) {
		tmp = ((double) (y * ((double) (t * ((double) (x - z))))));
	} else {
		double tmp_1;
		if ((((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t)) <= -1.579478125434173e-301)) {
			tmp_1 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
		} else {
			double tmp_2;
			if ((((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t)) <= 4.0591586060962483e-289)) {
				tmp_2 = ((double) (y * ((double) (t * ((double) (x - z))))));
			} else {
				double tmp_3;
				if ((((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t)) <= 2.728593090045186e+195)) {
					tmp_3 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
				} else {
					tmp_3 = ((double) (((double) (x - z)) * ((double) (y * t))));
				}
				tmp_2 = tmp_3;
			}
			tmp_1 = tmp_2;
		}
		tmp = tmp_1;
	}
	return tmp;
}

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
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 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < -inf.0 or -1.5794781254341731e-301 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < 4.05915860609624829e-289

    1. Initial program 19.5

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

    2. Simplified0.7

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

    if -inf.0 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < -1.5794781254341731e-301 or 4.05915860609624829e-289 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < 2.72859309004518595e195

    1. Initial program 0.4

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

    if 2.72859309004518595e195 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)

    1. Initial program 26.4

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

    2. Simplified13.9

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

    4. Applied associate-*r*_binary643.7

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -1.579478125434173 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 4.0591586060962483 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 2.728593090045186 \cdot 10^{+195}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))