Average Error: 2.0 → 2.0
Time: 20.5s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.073388601361955291545855403151588574509 \cdot 10^{-267} \lor \neg \left(y \le 1.188637650407096621287004044639126749192 \cdot 10^{-194}\right):\\ \;\;\;\;\left(\frac{x}{z - y} - \frac{y}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.073388601361955291545855403151588574509 \cdot 10^{-267} \lor \neg \left(y \le 1.188637650407096621287004044639126749192 \cdot 10^{-194}\right):\\
\;\;\;\;\left(\frac{x}{z - y} - \frac{y}{z - y}\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r267961 = x;
        double r267962 = y;
        double r267963 = r267961 - r267962;
        double r267964 = z;
        double r267965 = r267964 - r267962;
        double r267966 = r267963 / r267965;
        double r267967 = t;
        double r267968 = r267966 * r267967;
        return r267968;
}
↓
double f(double x, double y, double z, double t) {
        double r267969 = y;
        double r267970 = -1.0733886013619553e-267;
        bool r267971 = r267969 <= r267970;
        double r267972 = 1.1886376504070966e-194;
        bool r267973 = r267969 <= r267972;
        double r267974 = !r267973;
        bool r267975 = r267971 || r267974;
        double r267976 = x;
        double r267977 = z;
        double r267978 = r267977 - r267969;
        double r267979 = r267976 / r267978;
        double r267980 = r267969 / r267978;
        double r267981 = r267979 - r267980;
        double r267982 = t;
        double r267983 = r267981 * r267982;
        double r267984 = r267976 - r267969;
        double r267985 = r267984 * r267982;
        double r267986 = r267985 / r267978;
        double r267987 = r267975 ? r267983 : r267986;
        return r267987;
}

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

Original2.0
Target2.0
Herbie2.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.0733886013619553e-267 or 1.1886376504070966e-194 < y

    1. Initial program 1.5

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

    3. Applied div-sub1.5

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

    if -1.0733886013619553e-267 < y < 1.1886376504070966e-194

    1. Initial program 5.7

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

    3. Applied associate-*l/6.4

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.073388601361955291545855403151588574509 \cdot 10^{-267} \lor \neg \left(y \le 1.188637650407096621287004044639126749192 \cdot 10^{-194}\right):\\ \;\;\;\;\left(\frac{x}{z - y} - \frac{y}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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