Average Error: 7.3 → 2.0
Time: 3.3s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -8.860559052952926 \cdot 10^{+247} \lor \neg \left(x \cdot y - y \cdot z \leq 1.0771988499236273 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -8.860559052952926 \cdot 10^{+247} \lor \neg \left(x \cdot y - y \cdot z \leq 1.0771988499236273 \cdot 10^{+126}\right):\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

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

\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 (((((double) (((double) (x * y)) - ((double) (y * z)))) <= -8.860559052952926e+247) || !(((double) (((double) (x * y)) - ((double) (y * z)))) <= 1.0771988499236273e+126))) {
		VAR = ((double) (y * ((double) (t * ((double) (x - z))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
	}
	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

Original7.3
Target3.2
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -8.860559052952926e247 or 1.07719884992362732e126 < (- (* x y) (* z y))

    1. Initial program 25.7

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

    2. Simplified2.5

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

    if -8.860559052952926e247 < (- (* x y) (* z y)) < 1.07719884992362732e126

    1. Initial program 1.8

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -8.860559052952926 \cdot 10^{+247} \lor \neg \left(x \cdot y - y \cdot z \leq 1.0771988499236273 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))