Average Error: 6.9 → 1.4
Time: 7.1s
Precision: binary64
\[[y, t]=\mathsf{sort}([y, t])\]
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.124368088322739 \cdot 10^{+158} \lor \neg \left(x \cdot y - y \cdot z \leq 3.386096885892808 \cdot 10^{+202}\right):\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t - \left(y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -2.124368088322739 \cdot 10^{+158} \lor \neg \left(x \cdot y - y \cdot z \leq 3.386096885892808 \cdot 10^{+202}\right):\\
\;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\

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

\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)) -2.124368088322739e+158)
         (not (<= (- (* x y) (* y z)) 3.386096885892808e+202)))
   (* y (- (* x t) (* z t)))
   (- (* (* x y) t) (* (* y z) t))))
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)) <= -2.124368088322739e+158) || !(((x * y) - (y * z)) <= 3.386096885892808e+202)) {
		tmp = y * ((x * t) - (z * t));
	} else {
		tmp = ((x * y) * t) - ((y * z) * t);
	}
	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
Target3.1
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -2.124368088322739e158 or 3.3860968858928079e202 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 24.8

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

    2. Taylor expanded around 0 24.8

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

    3. Simplified24.8

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

    4. Taylor expanded around 0 1.1

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

    if -2.124368088322739e158 < (-.f64 (*.f64 x y) (*.f64 z y)) < 3.3860968858928079e202

    1. Initial program 1.5

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

    2. Taylor expanded around 0 1.5

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

    3. Simplified1.5

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

    5. Applied sub-neg_binary64_140521.5

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

    6. Applied distribute-rgt-in_binary64_140091.5

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

    7. Applied distribute-rgt-in_binary64_140091.5

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.124368088322739 \cdot 10^{+158} \lor \neg \left(x \cdot y - y \cdot z \leq 3.386096885892808 \cdot 10^{+202}\right):\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t - \left(y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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))