Average Error: 7.3 → 4.0
Time: 2.7s
Precision: binary64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 9.735236105864914 \cdot 10^{+54}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot 2 \leq 9.735236105864914 \cdot 10^{+54}:\\
\;\;\;\;\frac{2 \cdot \frac{x}{z}}{y - t}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (((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)) <= 9.735236105864914e+54)) {
		VAR = (((double) (2.0 * (x / z))) / ((double) (y - t)));
	} else {
		VAR = (((double) (x * (2.0 / ((double) (y - t))))) / z);
	}
	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
Target2.3
Herbie4.0
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < 1.0450278273301259 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x 2.0) < 9.73523610586491391e54

    1. Initial program 5.9

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

    2. Simplified4.8

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

    4. Applied *-un-lft-identity4.8

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

    5. Applied times-frac4.6

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

    6. Applied associate-*r*4.3

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

    7. Simplified4.2

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

    9. Applied associate-*r/4.2

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

    if 9.73523610586491391e54 < (* x 2.0)

    1. Initial program 13.3

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

    2. Simplified12.6

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

    4. Applied *-un-lft-identity12.6

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

    5. Applied times-frac11.8

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

    6. Applied associate-*r*12.6

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

    7. Simplified12.6

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

    9. Applied associate-*l/2.9

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 9.735236105864914 \cdot 10^{+54}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))