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 r444684 = x;
        double r444685 = y;
        double r444686 = r444684 - r444685;
        double r444687 = z;
        double r444688 = r444687 - r444685;
        double r444689 = r444686 / r444688;
        double r444690 = t;
        double r444691 = r444689 * r444690;
        return r444691;
}
↓
double f(double x, double y, double z, double t) {
        double r444692 = x;
        double r444693 = y;
        double r444694 = r444692 - r444693;
        double r444695 = z;
        double r444696 = r444695 - r444693;
        double r444697 = r444694 / r444696;
        double r444698 = -5.297791397205155e-210;
        bool r444699 = r444697 <= r444698;
        double r444700 = -0.0;
        bool r444701 = r444697 <= r444700;
        double r444702 = !r444701;
        bool r444703 = r444699 || r444702;
        double r444704 = t;
        double r444705 = r444697 * r444704;
        double r444706 = r444696 / r444704;
        double r444707 = r444694 / r444706;
        double r444708 = r444703 ? r444705 : r444707;
        return r444708;
}

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 un-div-inv0.8

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