Average Error: 7.0 → 0.5
Time: 33.0s
Precision: binary64
\[[y, t]=\mathsf{sort}([y, t])\]
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -4.3048303798646114 \cdot 10^{+132} \lor \neg \left(x \cdot y - y \cdot z \leq -4.671745387583375 \cdot 10^{-252} \lor \neg \left(x \cdot y - y \cdot z \leq 5.721197217844068 \cdot 10^{-255}\right) \land x \cdot y - y \cdot z \leq 1.700309588787803 \cdot 10^{+244}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -4.3048303798646114 \cdot 10^{+132} \lor \neg \left(x \cdot y - y \cdot z \leq -4.671745387583375 \cdot 10^{-252} \lor \neg \left(x \cdot y - y \cdot z \leq 5.721197217844068 \cdot 10^{-255}\right) \land x \cdot y - y \cdot z \leq 1.700309588787803 \cdot 10^{+244}\right):\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(y \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 (or (<= (- (* x y) (* y z)) -4.3048303798646114e+132)
         (not
          (or (<= (- (* x y) (* y z)) -4.671745387583375e-252)
              (and (not (<= (- (* x y) (* y z)) 5.721197217844068e-255))
                   (<= (- (* x y) (* y z)) 1.700309588787803e+244)))))
   (* (* y t) (- x z))
   (* t (* y (- 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)) <= -4.3048303798646114e+132) || !((((x * y) - (y * z)) <= -4.671745387583375e-252) || (!(((x * y) - (y * z)) <= 5.721197217844068e-255) && (((x * y) - (y * z)) <= 1.700309588787803e+244)))) {
		tmp = (y * t) * (x - z);
	} else {
		tmp = t * (y * (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

Original7.0
Target3.0
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 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -4.30483037986461139e132 or -4.67174538758337515e-252 < (-.f64 (*.f64 x y) (*.f64 z y)) < 5.72119721784406826e-255 or 1.7003095887878031e244 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 21.4

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

    2. Simplified1.2

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

    4. Applied associate-*r*_binary64_174091.1

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

    5. Simplified1.1

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

    if -4.30483037986461139e132 < (-.f64 (*.f64 x y) (*.f64 z y)) < -4.67174538758337515e-252 or 5.72119721784406826e-255 < (-.f64 (*.f64 x y) (*.f64 z y)) < 1.7003095887878031e244

    1. Initial program 0.2

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

    2. Simplified9.3

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

    3. Taylor expanded around 0 9.3

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

    4. Simplified0.2

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(x - z\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -4.3048303798646114 \cdot 10^{+132} \lor \neg \left(x \cdot y - y \cdot z \leq -4.671745387583375 \cdot 10^{-252} \lor \neg \left(x \cdot y - y \cdot z \leq 5.721197217844068 \cdot 10^{-255}\right) \land x \cdot y - y \cdot z \leq 1.700309588787803 \cdot 10^{+244}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021090 
(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))