Average Error: 7.4 → 2.7
Time: 2.9s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -873265403809526.125 \lor \neg \left(y \le 2.95791696916340278 \cdot 10^{-30}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot x + \left(t \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -873265403809526.125 \lor \neg \left(y \le 2.95791696916340278 \cdot 10^{-30}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot x + \left(t \cdot y\right) \cdot \left(-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 (((x * y) - (z * y)) * t);
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((y <= -873265403809526.1) || !(y <= 2.9579169691634028e-30))) {
		VAR = (((t * y) * x) + ((t * y) * -z));
	} 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

Original7.4
Target3.0
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -873265403809526.1 or 2.9579169691634028e-30 < y

    1. Initial program 14.9

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

    2. Simplified14.9

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

    4. Applied associate-*r*3.3

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

    6. Applied sub-neg3.3

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

    7. Applied distribute-lft-in3.3

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

    if -873265403809526.1 < y < 2.9579169691634028e-30

    1. Initial program 2.3

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

    2. Simplified2.3

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -873265403809526.125 \lor \neg \left(y \le 2.95791696916340278 \cdot 10^{-30}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot x + \left(t \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(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))