Average Error: 7.1 → 3.0
Time: 6.5s
Precision: binary64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4.9660709412788435 \cdot 10^{-216} \lor \neg \left(x \cdot 2 \leq 15670887.655105175\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot 2 \leq -4.9660709412788435 \cdot 10^{-216} \lor \neg \left(x \cdot 2 \leq 15670887.655105175\right):\\
\;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\

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

\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 (<= (* x 2.0) -4.9660709412788435e-216)
         (not (<= (* x 2.0) 15670887.655105175)))
   (/ (/ (* x 2.0) (- y t)) z)
   (/ (* x 2.0) (* (- y t) z))))
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 (((x * 2.0) <= -4.9660709412788435e-216) || !((x * 2.0) <= 15670887.655105175)) {
		tmp = ((x * 2.0) / (y - t)) / z;
	} else {
		tmp = (x * 2.0) / ((y - t) * z);
	}
	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

Original7.1
Target2.1
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < 1.0450278273301259 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 x 2) < -4.9660709412788435e-216 or 15670887.6551051755 < (*.f64 x 2)

    1. Initial program 9.2

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

    2. Simplified7.7

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

    4. Applied associate-*r/_binary64_155013.5

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

    6. Applied associate-*r/_binary64_155013.5

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

    if -4.9660709412788435e-216 < (*.f64 x 2) < 15670887.6551051755

    1. Initial program 3.4

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

    2. Simplified2.3

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

    4. Applied associate-*r/_binary64_155017.9

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

    6. Applied associate-*r/_binary64_155017.8

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

    7. Applied associate-/l/_binary64_155062.1

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

    8. Simplified2.1

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4.9660709412788435 \cdot 10^{-216} \lor \neg \left(x \cdot 2 \leq 15670887.655105175\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020277 
(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))))