Average Error: 6.6 → 2.4
Time: 3.6s
Precision: binary64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -3.707866008615156 \cdot 10^{-76} \lor \neg \left(x \cdot 2 \leq 11433628.305164771\right):\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot 2 \leq -3.707866008615156 \cdot 10^{-76} \lor \neg \left(x \cdot 2 \leq 11433628.305164771\right):\\
\;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot 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)) <= -3.707866008615156e-76) || !(((double) (x * 2.0)) <= 11433628.305164771))) {
		VAR = (((double) (x * (2.0 / ((double) (y - t))))) / z);
	} else {
		VAR = (((double) (x * 2.0)) / ((double) (((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

Original6.6
Target2.1
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < 1.0450278273301259 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x 2.0) < -3.70786600861515622e-76 or 11433628.3051647712 < (* x 2.0)

    1. Initial program 9.6

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

    2. Simplified8.9

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

    4. Applied *-un-lft-identity8.9

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

    5. Applied times-frac8.5

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

    6. Applied associate-*r*9.5

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

    7. Simplified9.4

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

    9. Applied associate-*l/2.7

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

    if -3.70786600861515622e-76 < (* x 2.0) < 11433628.3051647712

    1. Initial program 3.2

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

    2. Simplified2.4

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

    4. Applied associate-*r/2.1

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -3.707866008615156 \cdot 10^{-76} \lor \neg \left(x \cdot 2 \leq 11433628.305164771\right):\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z}\\ \end{array}\]

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))))