Average Error: 7.6 → 3.5
Time: 2.6s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\
\;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\

\mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (((x * y) - (z * y)) * t);
}
↓
double code(double x, double y, double z, double t) {
	double temp;
	if ((y <= -1.434059461590054e-73)) {
		temp = (((x - z) * t) * y);
	} else {
		double temp_1;
		if ((y <= 8.822188301346798e-152)) {
			temp_1 = (t * (y * (x - z)));
		} else {
			temp_1 = ((x - z) * (t * y));
		}
		temp = temp_1;
	}
	return temp;
}

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

Original7.6
Target3.1
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.434059461590054e-73

    1. Initial program 12.4

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

    2. Simplified12.4

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

    3. Taylor expanded around inf 12.4

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

    4. Simplified3.6

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

    6. Applied associate-*r*3.5

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

    if -1.434059461590054e-73 < y < 8.822188301346798e-152

    1. Initial program 2.9

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

    2. Simplified2.9

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

    if 8.822188301346798e-152 < y

    1. Initial program 9.7

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

    2. Simplified9.7

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

    3. Taylor expanded around inf 9.7

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

    4. Simplified4.3

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))