Average Error: 6.7 → 2.5
Time: 11.4s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.20052350072620737692343564222038722076 \cdot 10^{-21} \lor \neg \left(z \le 7.10776943103653364138280811307393783598 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot \left(y - t\right)}{x \cdot 2}}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.20052350072620737692343564222038722076 \cdot 10^{-21} \lor \neg \left(z \le 7.10776943103653364138280811307393783598 \cdot 10^{-114}\right):\\
\;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z \cdot \left(y - t\right)}{x \cdot 2}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r384819 = x;
        double r384820 = 2.0;
        double r384821 = r384819 * r384820;
        double r384822 = y;
        double r384823 = z;
        double r384824 = r384822 * r384823;
        double r384825 = t;
        double r384826 = r384825 * r384823;
        double r384827 = r384824 - r384826;
        double r384828 = r384821 / r384827;
        return r384828;
}
↓
double f(double x, double y, double z, double t) {
        double r384829 = z;
        double r384830 = -2.2005235007262074e-21;
        bool r384831 = r384829 <= r384830;
        double r384832 = 7.107769431036534e-114;
        bool r384833 = r384829 <= r384832;
        double r384834 = !r384833;
        bool r384835 = r384831 || r384834;
        double r384836 = x;
        double r384837 = 2.0;
        double r384838 = r384836 * r384837;
        double r384839 = r384838 / r384829;
        double r384840 = y;
        double r384841 = t;
        double r384842 = r384840 - r384841;
        double r384843 = r384839 / r384842;
        double r384844 = 1.0;
        double r384845 = r384829 * r384842;
        double r384846 = r384845 / r384838;
        double r384847 = r384844 / r384846;
        double r384848 = r384835 ? r384843 : r384847;
        return r384848;
}

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
Target2.1
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061113708240820439530037456 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.045027827330126029709547581125571222799 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.2005235007262074e-21 or 7.107769431036534e-114 < z

    1. Initial program 8.8

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

    2. Simplified7.1

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

    4. Applied associate-/r*2.1

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

    if -2.2005235007262074e-21 < z < 7.107769431036534e-114

    1. Initial program 2.9

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

    2. Simplified2.9

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

    4. Applied clear-num3.3

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot \left(y - t\right)}{x \cdot 2}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.20052350072620737692343564222038722076 \cdot 10^{-21} \lor \neg \left(z \le 7.10776943103653364138280811307393783598 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot \left(y - t\right)}{x \cdot 2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))