Average Error: 7.3 → 2.7
Time: 3.4s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -457558530138193790 \lor \neg \left(t \le 1.1602899051058606 \cdot 10^{-11}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le -457558530138193790 \lor \neg \left(t \le 1.1602899051058606 \cdot 10^{-11}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

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

\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 <= -4.575585301381938e+17) || !(t <= 1.1602899051058606e-11))) {
		VAR = ((double) (((double) (t * y)) * ((double) (x - z))));
	} else {
		VAR = ((double) (((double) (t * ((double) (x - z)))) * y));
	}
	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
Target2.9
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.575585301381938e+17 or 1.1602899051058606e-11 < t

    1. Initial program 3.4

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

    2. Simplified3.4

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

    4. Applied associate-*r*3.8

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

    if -4.575585301381938e+17 < t < 1.1602899051058606e-11

    1. Initial program 9.6

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

    2. Simplified9.6

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

    4. Applied add-cube-cbrt10.4

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

    5. Applied associate-*r*10.3

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

    7. Applied add-cube-cbrt10.6

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

    8. Applied associate-*l*10.6

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

    9. Simplified6.9

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

    11. Applied associate-*r*3.1

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

    12. Simplified2.1

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -457558530138193790 \lor \neg \left(t \le 1.1602899051058606 \cdot 10^{-11}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020120 
(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))