Average Error: 6.9 → 0.9
Time: 8.9s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z - t \cdot z \le -2.0148370340377071 \cdot 10^{171}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le -4.723901171503675 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 9.15232862407595114 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 1.16814661386677839 \cdot 10^{214}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z - t \cdot z \le -2.0148370340377071 \cdot 10^{171}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le -4.723901171503675 \cdot 10^{-94}:\\
\;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le 9.15232862407595114 \cdot 10^{-285}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le 1.16814661386677839 \cdot 10^{214}:\\
\;\;\;\;\frac{x \cdot 2}{y \cdot z - t \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((x * 2.0) / ((y * z) - (t * z)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((y * z) - (t * z)) <= -2.014837034037707e+171)) {
		VAR = ((x / z) / ((y - t) / 2.0));
	} else {
		double VAR_1;
		if ((((y * z) - (t * z)) <= -4.723901171503675e-94)) {
			VAR_1 = (x * ((2.0 / (y - t)) / z));
		} else {
			double VAR_2;
			if ((((y * z) - (t * z)) <= 9.152328624075951e-285)) {
				VAR_2 = ((x / z) / ((y - t) / 2.0));
			} else {
				double VAR_3;
				if ((((y * z) - (t * z)) <= 1.1681466138667784e+214)) {
					VAR_3 = ((x * 2.0) / ((y * z) - (t * z)));
				} else {
					VAR_3 = ((x / z) / ((y - t) / 2.0));
				}
				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

Original6.9
Target2.3
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.04502782733012586 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* y z) (* t z)) < -2.014837034037707e+171 or -4.723901171503675e-94 < (- (* y z) (* t z)) < 9.152328624075951e-285 or 1.1681466138667784e+214 < (- (* y z) (* t z))

    1. Initial program 14.4

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified11.9

      \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity11.9

      \[\leadsto \frac{x}{\frac{z \cdot \left(y - t\right)}{\color{blue}{1 \cdot 2}}}\]

    5. Applied times-frac11.9

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{1} \cdot \frac{y - t}{2}}}\]

    6. Applied associate-/r*1.6

      \[\leadsto \color{blue}{\frac{\frac{x}{\frac{z}{1}}}{\frac{y - t}{2}}}\]

    7. Simplified1.6

      \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\frac{y - t}{2}}\]

    if -2.014837034037707e+171 < (- (* y z) (* t z)) < -4.723901171503675e-94

    1. Initial program 0.2

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified0.2

      \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}}\]
    3. Using strategy rm

    4. Applied div-inv0.3

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z \cdot \left(y - t\right)}{2}}}\]

    5. Simplified0.3

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}}\]

    if 9.152328624075951e-285 < (- (* y z) (* t z)) < 1.1681466138667784e+214

    1. Initial program 0.2

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - t \cdot z \le -2.0148370340377071 \cdot 10^{171}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le -4.723901171503675 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 9.15232862407595114 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 1.16814661386677839 \cdot 10^{214}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))