Average Error: 7.1 → 1.3
Time: 3.6s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -3.2255344406562545 \cdot 10^{+294}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.307694149260909 \cdot 10^{+181}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -3.2255344406562545 \cdot 10^{+294}:\\
\;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 1.307694149260909 \cdot 10^{+181}:\\
\;\;\;\;\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)) -3.2255344406562545e+294)
   (- (* y (* x t)) (* y (* z t)))
   (if (<= (- (* x y) (* y z)) 1.307694149260909e+181)
     (* (- (* 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)) <= -3.2255344406562545e+294) {
		tmp = (y * (x * t)) - (y * (z * t));
	} else if (((x * y) - (y * z)) <= 1.307694149260909e+181) {
		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

Original7.1
Target3.1
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -3.2255344406562545e294

    1. Initial program 55.6

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

    2. Simplified0.3

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

    4. Applied sub-neg_binary640.3

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

    5. Applied distribute-rgt-in_binary640.3

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

    6. Applied distribute-rgt-in_binary640.3

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

    7. Simplified0.3

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

    8. Simplified0.3

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

    if -3.2255344406562545e294 < (-.f64 (*.f64 x y) (*.f64 z y)) < 1.30769414926090905e181

    1. Initial program 1.4

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

    if 1.30769414926090905e181 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 26.9

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

    2. Simplified1.5

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

    4. Applied associate-*r*_binary641.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -3.2255344406562545 \cdot 10^{+294}:\\ \;\;\;\;y \cdot \left(x \cdot t\right) - y \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.307694149260909 \cdot 10^{+181}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020260 
(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))