Average Error: 6.7 → 2.5
Time: 6.6s
Precision: binary64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot 2 \le -1.7261318963864587 \cdot 10^{-129} \lor \neg \left(x \cdot 2 \le 1.8045065908215711 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot 2 \le -1.7261318963864587 \cdot 10^{-129} \lor \neg \left(x \cdot 2 \le 1.8045065908215711 \cdot 10^{-24}\right):\\
\;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * 2.0)) / ((double) (((double) (y * z)) - ((double) (t * z))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x * 2.0)) <= -1.7261318963864587e-129) || !(((double) (x * 2.0)) <= 1.804506590821571e-24))) {
		VAR = ((double) (((double) (((double) (x * 2.0)) / ((double) (y - t)))) / z));
	} else {
		VAR = ((double) (x / ((double) (((double) (z * ((double) (y - t)))) / 2.0))));
	}
	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

Original6.7
Target2.2
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.04502782733012586 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x 2.0) < -1.7261318963864587e-129 or 1.8045065908215711e-24 < (* x 2.0)

    1. Initial program 9.0

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

    2. Simplified7.8

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

    4. Applied div-inv8.0

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

    5. Simplified7.4

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}}\]
    6. Using strategy rm

    7. Applied associate-*r/2.9

      \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}}\]
    8. Using strategy rm

    9. Applied associate-*r/2.8

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

    if -1.7261318963864587e-129 < (* x 2.0) < 1.8045065908215711e-24

    1. Initial program 3.4

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

    2. Simplified2.0

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \le -1.7261318963864587 \cdot 10^{-129} \lor \neg \left(x \cdot 2 \le 1.8045065908215711 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))