Average Error: 7.1 → 0.5
Time: 3.9s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.2358054952721706 \cdot 10^{+267}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -4.1781965840692 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.063912548893415 \cdot 10^{-199}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 9.24235344701696 \cdot 10^{+170}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -1.2358054952721706 \cdot 10^{+267}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -4.1781965840692 \cdot 10^{-210}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 5.063912548893415 \cdot 10^{-199}:\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 9.24235344701696 \cdot 10^{+170}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\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)) -1.2358054952721706e+267)
   (* y (* t (- x z)))
   (if (<= (- (* x y) (* y z)) -4.1781965840692e-210)
     (* (- (* x y) (* y z)) t)
     (if (<= (- (* x y) (* y z)) 5.063912548893415e-199)
       (* (- x z) (* y t))
       (if (<= (- (* x y) (* y z)) 9.24235344701696e+170)
         (* (- (* x y) (* y z)) t)
         (* y (* t (- x z))))))))
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) (x * y)) - ((double) (y * z)))) <= -1.2358054952721706e+267)) {
		tmp = ((double) (y * ((double) (t * ((double) (x - z))))));
	} else {
		double tmp_1;
		if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= -4.1781965840692e-210)) {
			tmp_1 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
		} else {
			double tmp_2;
			if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 5.063912548893415e-199)) {
				tmp_2 = ((double) (((double) (x - z)) * ((double) (y * t))));
			} else {
				double tmp_3;
				if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 9.24235344701696e+170)) {
					tmp_3 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
				} else {
					tmp_3 = ((double) (y * ((double) (t * ((double) (x - z))))));
				}
				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

Original7.1
Target3.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -1.23580549527217057e267 or 9.24235344701695991e170 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 31.9

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

    2. Simplified1.4

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

    if -1.23580549527217057e267 < (-.f64 (*.f64 x y) (*.f64 z y)) < -4.1781965840691998e-210 or 5.0639125488934151e-199 < (-.f64 (*.f64 x y) (*.f64 z y)) < 9.24235344701695991e170

    1. Initial program 0.3

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

    if -4.1781965840691998e-210 < (-.f64 (*.f64 x y) (*.f64 z y)) < 5.0639125488934151e-199

    1. Initial program 8.7

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

    2. Simplified0.6

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

    4. Applied associate-*r*_binary640.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.2358054952721706 \cdot 10^{+267}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -4.1781965840692 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.063912548893415 \cdot 10^{-199}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 9.24235344701696 \cdot 10^{+170}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))