Average Error: 2.3 → 1.6
Time: 15.7s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\mathbf{else}:\\
\;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r305885 = x;
        double r305886 = y;
        double r305887 = r305885 - r305886;
        double r305888 = z;
        double r305889 = r305888 - r305886;
        double r305890 = r305887 / r305889;
        double r305891 = t;
        double r305892 = r305890 * r305891;
        return r305892;
}
↓
double f(double x, double y, double z, double t) {
        double r305893 = x;
        double r305894 = y;
        double r305895 = r305893 - r305894;
        double r305896 = z;
        double r305897 = r305896 - r305894;
        double r305898 = r305895 / r305897;
        double r305899 = -5.297791397205155e-210;
        bool r305900 = r305898 <= r305899;
        double r305901 = -0.0;
        bool r305902 = r305898 <= r305901;
        double r305903 = !r305902;
        bool r305904 = r305900 || r305903;
        double r305905 = t;
        double r305906 = r305898 * r305905;
        double r305907 = r305897 / r305905;
        double r305908 = r305895 / r305907;
        double r305909 = r305904 ? r305906 : r305908;
        return r305909;
}

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

Original2.3
Target2.3
Herbie1.6
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -5.297791397205155e-210 or -0.0 < (/ (- x y) (- z y))

    1. Initial program 2.0

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

    if -5.297791397205155e-210 < (/ (- x y) (- z y)) < -0.0

    1. Initial program 7.7

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

    3. Applied div-inv7.8

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

    4. Applied associate-*l*0.9

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

    5. Simplified0.8

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

    7. Applied clear-num0.9

      \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{1}{\frac{z - y}{t}}}\]
    8. Using strategy rm

    9. Applied pow10.9

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

    10. Applied pow10.9

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

    11. Applied pow-prod-down0.9

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

    12. Simplified0.8

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +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))