Average Error: 6.9 → 0.6
Time: 3.8s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -2.528554632800738 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.742997195573958 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 2.0277330427960423 \cdot 10^{+192}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -2.528554632800738 \cdot 10^{-156}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 1.742997195573958 \cdot 10^{-261}:\\
\;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 2.0277330427960423 \cdot 10^{+192}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\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)) (- INFINITY))
   (* (* y t) (- x z))
   (if (<= (- (* x y) (* y z)) -2.528554632800738e-156)
     (* (- (* x y) (* y z)) t)
     (if (<= (- (* x y) (* y z)) 1.742997195573958e-261)
       (- (* y (* x t)) (* y (* z t)))
       (if (<= (- (* x y) (* y z)) 2.0277330427960423e+192)
         (* (- (* x y) (* y z)) t)
         (* (* y t) (- x z)))))))
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 tmp;
	if (((x * y) - (y * z)) <= -((double) INFINITY)) {
		tmp = (y * t) * (x - z);
	} else if (((x * y) - (y * z)) <= -2.528554632800738e-156) {
		tmp = ((x * y) - (y * z)) * t;
	} else if (((x * y) - (y * z)) <= 1.742997195573958e-261) {
		tmp = (y * (x * t)) - (y * (z * t));
	} else if (((x * y) - (y * z)) <= 2.0277330427960423e+192) {
		tmp = ((x * y) - (y * z)) * t;
	} else {
		tmp = (y * t) * (x - z);
	}
	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

Original6.9
Target3.2
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -inf.0 or 2.02773304279604234e192 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 36.9

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

    2. Simplified1.1

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

    4. Applied associate-*r*_binary641.4

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

    if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z y)) < -2.52855463280073819e-156 or 1.74299719557395796e-261 < (-.f64 (*.f64 x y) (*.f64 z y)) < 2.02773304279604234e192

    1. Initial program 0.2

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

    if -2.52855463280073819e-156 < (-.f64 (*.f64 x y) (*.f64 z y)) < 1.74299719557395796e-261

    1. Initial program 8.4

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

    2. Simplified1.4

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

    4. Applied sub-neg_binary641.4

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

    5. Applied distribute-rgt-in_binary641.4

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

    6. Applied distribute-rgt-in_binary641.4

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

    7. Simplified1.4

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

    8. Simplified1.4

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -2.528554632800738 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.742997195573958 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 2.0277330427960423 \cdot 10^{+192}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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))