Average Error: 6.8 → 1.2
Time: 4.2s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -9.6798190984459013 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 9.87793409643828 \cdot 10^{-95}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 7.8191553873519319 \cdot 10^{273}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -9.6798190984459013 \cdot 10^{-73}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 9.87793409643828 \cdot 10^{-95}:\\
\;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 7.8191553873519319 \cdot 10^{273}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\

\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 ((((double) (((double) (x * y)) - ((double) (z * y)))) <= -inf.0)) {
		VAR = ((double) (y * ((double) (((double) (x - z)) * t))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (z * y)))) <= -9.679819098445901e-73)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * y)) - ((double) (z * y)))) <= 9.87793409643828e-95)) {
				VAR_2 = ((double) pow(((double) (((double) (t * y)) * ((double) (x - z)))), 1.0));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * y)) - ((double) (z * y)))) <= 7.819155387351932e+273)) {
					VAR_3 = ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
				} else {
					VAR_3 = ((double) pow(((double) (((double) (t * y)) * ((double) (x - z)))), 1.0));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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

Original6.8
Target3.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-commutative64.0

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

    4. Applied *-commutative64.0

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

    5. Applied distribute-lft-out--64.0

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

    6. Applied associate-*l*0.2

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

    if -inf.0 < (- (* x y) (* z y)) < -9.679819098445901e-73 or 9.87793409643828e-95 < (- (* x y) (* z y)) < 7.819155387351932e+273

    1. Initial program 0.3

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

    if -9.679819098445901e-73 < (- (* x y) (* z y)) < 9.87793409643828e-95 or 7.819155387351932e+273 < (- (* x y) (* z y))

    1. Initial program 11.7

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

    3. Applied pow111.7

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

    4. Applied pow111.7

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

    5. Applied pow-prod-down11.7

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

    6. Simplified2.9

      \[\leadsto {\color{blue}{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -9.6798190984459013 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 9.87793409643828 \cdot 10^{-95}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 7.8191553873519319 \cdot 10^{273}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 +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))