Average Error: 6.9 → 3.1
Time: 6.8s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.2960282936665467 \cdot 10^{66}:\\ \;\;\;\;\left(y \cdot \left(\left(\left(x - z\right) \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}\\ \mathbf{elif}\;y \le 5.66449528431328841 \cdot 10^{35}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.2960282936665467 \cdot 10^{66}:\\
\;\;\;\;\left(y \cdot \left(\left(\left(x - z\right) \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}\\

\mathbf{elif}\;y \le 5.66449528431328841 \cdot 10^{35}:\\
\;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\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 <= -3.2960282936665467e+66)) {
		VAR = ((double) (((double) (y * ((double) (((double) (((double) (x - z)) * ((double) cbrt(t)))) * ((double) cbrt(t)))))) * ((double) cbrt(t))));
	} else {
		double VAR_1;
		if ((y <= 5.6644952843132884e+35)) {
			VAR_1 = ((double) (((double) (y * ((double) (x - z)))) * t));
		} else {
			VAR_1 = ((double) (y * ((double) (((double) (x - z)) * t))));
		}
		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

Original6.9
Target3.0
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.2960282936665467e66

    1. Initial program 20.1

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

    2. Simplified20.1

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

    4. Applied add-cube-cbrt20.9

      \[\leadsto \left(y \cdot \left(x - z\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

    5. Applied associate-*r*20.9

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

    7. Applied associate-*l*7.6

      \[\leadsto \color{blue}{\left(y \cdot \left(\left(x - z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)\right)} \cdot \sqrt[3]{t}\]

    8. Simplified7.6

      \[\leadsto \left(y \cdot \color{blue}{\left(\left(\left(x - z\right) \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right) \cdot \sqrt[3]{t}\]

    if -3.2960282936665467e66 < y < 5.66449528431328841e35

    1. Initial program 2.1

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

    2. Simplified2.1

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

    if 5.66449528431328841e35 < y

    1. Initial program 16.9

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

    2. Simplified16.9

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

    4. Applied associate-*l*3.4

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.2960282936665467 \cdot 10^{66}:\\ \;\;\;\;\left(y \cdot \left(\left(\left(x - z\right) \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}\\ \mathbf{elif}\;y \le 5.66449528431328841 \cdot 10^{35}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))