Average Error: 6.8 → 5.0
Time: 4.6s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.078127285590954 \cdot 10^{-134} \lor \neg \left(t \le 3.8144823940086207 \cdot 10^{-267}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(y \cdot \left(\left(x - z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.078127285590954 \cdot 10^{-134} \lor \neg \left(t \le 3.8144823940086207 \cdot 10^{-267}\right):\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{t} \cdot \left(y \cdot \left(\left(x - z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\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 (((t <= -1.078127285590954e-134) || !(t <= 3.8144823940086207e-267))) {
		VAR = ((double) (t * ((double) (y * ((double) (x - z))))));
	} else {
		VAR = ((double) (((double) cbrt(t)) * ((double) (y * ((double) (((double) (x - z)) * ((double) (((double) cbrt(t)) * ((double) cbrt(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

Original6.8
Target3.0
Herbie5.0
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.078127285590954e-134 or 3.8144823940086207e-267 < t

    1. Initial program 5.3

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied *-un-lft-identity5.3

      \[\leadsto \left(x \cdot y - z \cdot y\right) \cdot \color{blue}{\left(1 \cdot t\right)}\]

    4. Applied associate-*r*5.3

      \[\leadsto \color{blue}{\left(\left(x \cdot y - z \cdot y\right) \cdot 1\right) \cdot t}\]

    5. Simplified5.3

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

    if -1.078127285590954e-134 < t < 3.8144823940086207e-267

    1. Initial program 12.0

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied add-cube-cbrt12.7

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

    4. Applied associate-*r*12.7

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

    5. Simplified4.2

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

  4. Final simplification5.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.078127285590954 \cdot 10^{-134} \lor \neg \left(t \le 3.8144823940086207 \cdot 10^{-267}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(y \cdot \left(\left(x - z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))