Average Error: 7.3 → 4.5
Time: 2.7s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.8977022651582564 \cdot 10^{-63} \lor \neg \left(y \le 1.21955483733648284 \cdot 10^{-250}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(y \cdot \left(x - z\right)\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.8977022651582564 \cdot 10^{-63} \lor \neg \left(y \le 1.21955483733648284 \cdot 10^{-250}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(y \cdot \left(x - z\right)\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 <= -1.8977022651582564e-63) || !(y <= 1.2195548373364828e-250))) {
		VAR = ((double) (((double) (t * y)) * ((double) (x - z))));
	} else {
		VAR = ((double) (((double) (((double) cbrt(t)) * ((double) cbrt(t)))) * ((double) (((double) cbrt(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

Original7.3
Target3.2
Herbie4.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.8977022651582564e-63 or 1.2195548373364828e-250 < y

    1. Initial program 9.1

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

    2. Simplified9.1

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

    4. Applied associate-*r*4.7

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

    if -1.8977022651582564e-63 < y < 1.2195548373364828e-250

    1. Initial program 3.3

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

    2. Simplified3.3

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

    4. Applied add-cube-cbrt4.1

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

    5. Applied associate-*l*4.1

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

  4. Final simplification4.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.8977022651582564 \cdot 10^{-63} \lor \neg \left(y \le 1.21955483733648284 \cdot 10^{-250}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(y \cdot \left(x - z\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020122 
(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))