Average Error: 6.8 → 2.8
Time: 3.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.4378417441544193 \cdot 10^{-9} \lor \neg \left(y \le 3.9938178602684773 \cdot 10^{-104}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.4378417441544193 \cdot 10^{-9} \lor \neg \left(y \le 3.9938178602684773 \cdot 10^{-104}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((y <= -5.437841744154419e-09) || !(y <= 3.993817860268477e-104))) {
		VAR = ((double) (((double) (t * y)) * ((double) (x - z))));
	} else {
		VAR = ((double) (t * ((double) (y * ((double) (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

Original6.8
Target2.8
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.437841744154419e-09 or 3.993817860268477e-104 < y

    1. Initial program 11.9

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

    2. Simplified11.9

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

    4. Applied associate-*r*3.7

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

    if -5.437841744154419e-09 < y < 3.993817860268477e-104

    1. Initial program 1.9

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

    2. Simplified1.9

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.4378417441544193 \cdot 10^{-9} \lor \neg \left(y \le 3.9938178602684773 \cdot 10^{-104}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 
(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))