Average Error: 6.7 → 4.7
Time: 4.7s
Precision: binary64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.2678525880262989 \cdot 10^{+64} \lor \neg \left(z \leq -6.187154742046292 \cdot 10^{-207}\right):\\ \;\;\;\;\left(x \cdot \frac{2}{y - t}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.2678525880262989 \cdot 10^{+64} \lor \neg \left(z \leq -6.187154742046292 \cdot 10^{-207}\right):\\
\;\;\;\;\left(x \cdot \frac{2}{y - t}\right) \cdot \frac{1}{z}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2678525880262989e+64) (not (<= z -6.187154742046292e-207)))
   (* (* x (/ 2.0 (- y t))) (/ 1.0 z))
   (/ (* x 2.0) (* z (- y t)))))
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 tmp;
	if ((z <= -1.2678525880262989e+64) || !(z <= -6.187154742046292e-207)) {
		tmp = (x * (2.0 / (y - t))) * (1.0 / z);
	} else {
		tmp = (x * 2.0) / (z * (y - t));
	}
	return tmp;
}

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
Herbie4.7
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < 1.0450278273301259 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2678525880262989e64 or -6.1871547420462918e-207 < z

    1. Initial program 8.2

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

    2. Simplified6.6

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

    4. Applied div-inv_binary646.6

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

    5. Applied associate-*r*_binary645.5

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

    if -1.2678525880262989e64 < z < -6.1871547420462918e-207

    1. Initial program 1.6

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

    2. Simplified1.7

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

    4. Applied associate-*r/_binary644.7

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

    6. Applied associate-*r/_binary644.7

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

    7. Applied associate-/l/_binary641.6

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

    8. Simplified1.6

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

  4. Final simplification4.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2678525880262989 \cdot 10^{+64} \lor \neg \left(z \leq -6.187154742046292 \cdot 10^{-207}\right):\\ \;\;\;\;\left(x \cdot \frac{2}{y - t}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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))))