Average Error: 7.2 → 0.6
Time: 3.7s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.9664886418725277 \cdot 10^{+168}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -6.785753350675336 \cdot 10^{-190}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.049820563907331 \cdot 10^{+238}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -2.9664886418725277 \cdot 10^{+168}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -6.785753350675336 \cdot 10^{-190}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 5.049820563907331 \cdot 10^{+238}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(t \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 ((((double) (((double) (x * y)) - ((double) (y * z)))) <= -2.9664886418725277e+168)) {
		VAR = ((double) (((double) (y * t)) * ((double) (x - z))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= -6.785753350675336e-190)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 0.0)) {
				VAR_2 = ((double) (((double) (y * t)) * ((double) (x - z))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * y)) - ((double) (y * z)))) <= 5.049820563907331e+238)) {
					VAR_3 = ((double) (((double) (((double) (x * y)) - ((double) (y * z)))) * t));
				} else {
					VAR_3 = ((double) (y * ((double) (t * ((double) (x - z))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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
Target3.0
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -2.9664886418725277e168 or -6.78575335067533551e-190 < (- (* x y) (* z y)) < 0.0

    1. Initial program 18.1

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

    2. Simplified1.5

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

    4. Applied associate-*r*1.4

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

    if -2.9664886418725277e168 < (- (* x y) (* z y)) < -6.78575335067533551e-190 or 0.0 < (- (* x y) (* z y)) < 5.04982056390733104e238

    1. Initial program 0.3

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

    if 5.04982056390733104e238 < (- (* x y) (* z y))

    1. Initial program 37.1

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

    2. Simplified0.8

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -2.9664886418725277 \cdot 10^{+168}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -6.785753350675336 \cdot 10^{-190}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.049820563907331 \cdot 10^{+238}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

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))