Average Error: 7.2 → 6.9
Time: 3.0s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.24575917908999902 \cdot 10^{-256} \lor \neg \left(t \le 4.3778532579656104 \cdot 10^{-196} \lor \neg \left(t \le 4.68042860704807678 \cdot 10^{145}\right)\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right) + t \cdot \left(\left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.24575917908999902 \cdot 10^{-256} \lor \neg \left(t \le 4.3778532579656104 \cdot 10^{-196} \lor \neg \left(t \le 4.68042860704807678 \cdot 10^{145}\right)\right):\\
\;\;\;\;t \cdot \left(x \cdot y\right) + t \cdot \left(\left(-z\right) \cdot y\right)\\

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

\end{array}
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 VAR;
	if (((t <= -1.245759179089999e-256) || !((t <= 4.37785325796561e-196) || !(t <= 4.680428607048077e+145)))) {
		VAR = ((t * (x * y)) + (t * (-z * y)));
	} else {
		VAR = ((t * y) * (x - z));
	}
	return VAR;
}

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

Original7.2
Target3.1
Herbie6.9
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.245759179089999e-256 or 4.37785325796561e-196 < t < 4.680428607048077e+145

    1. Initial program 5.9

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

    2. Simplified5.9

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

    4. Applied sub-neg5.9

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

    5. Applied distribute-lft-in5.9

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

    6. Applied distribute-lft-in5.9

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

    7. Simplified5.9

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

    8. Simplified5.9

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

    if -1.245759179089999e-256 < t < 4.37785325796561e-196 or 4.680428607048077e+145 < t

    1. Initial program 10.8

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

    2. Simplified10.8

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

    4. Applied associate-*r*9.5

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

  4. Final simplification6.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.24575917908999902 \cdot 10^{-256} \lor \neg \left(t \le 4.3778532579656104 \cdot 10^{-196} \lor \neg \left(t \le 4.68042860704807678 \cdot 10^{145}\right)\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right) + t \cdot \left(\left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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))