Average Error: 7.4 → 1.4
Time: 8.0s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t \]
↓
\[\begin{array}{l} t_1 := x \cdot y - y \cdot z\\ \mathbf{if}\;t_1 \leq -9.556989031823118 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 1.1558522186003537 \cdot 10^{+308}:\\ \;\;\;\;t_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
t_1 := x \cdot y - y \cdot z\\
\mathbf{if}\;t_1 \leq -9.556989031823118 \cdot 10^{+251}:\\
\;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\

\mathbf{elif}\;t_1 \leq 1.1558522186003537 \cdot 10^{+308}:\\
\;\;\;\;t_1 \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
 (let* ((t_1 (- (* x y) (* y z))))
   (if (<= t_1 -9.556989031823118e+251)
     (* y (- (* x t) (* z t)))
     (if (<= t_1 1.1558522186003537e+308) (* t_1 t) (* (- x z) (* y 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 t_1 = (x * y) - (y * z);
	double tmp;
	if (t_1 <= -9.556989031823118e+251) {
		tmp = y * ((x * t) - (z * t));
	} else if (t_1 <= 1.1558522186003537e+308) {
		tmp = t_1 * t;
	} else {
		tmp = (x - z) * (y * 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

Original7.4
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 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -9.5569890318231175e251

    1. Initial program 40.2

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

    2. Simplified0.4

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

    3. Taylor expanded in x around 0 0.4

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

    if -9.5569890318231175e251 < (-.f64 (*.f64 x y) (*.f64 z y)) < 1.15585221860035371e308

    1. Initial program 1.5

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

    if 1.15585221860035371e308 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 64.0

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

    2. Simplified0.2

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

    3. Taylor expanded in y around inf 0.3

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -9.556989031823118 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.1558522186003537 \cdot 10^{+308}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2021280 
(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))