Average Error: 11.7 → 2.5
Time: 12.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -821599116430925941436114357920196460544:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \mathbf{elif}\;z \le 5.862038722875420925631635452195167558109 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -821599116430925941436114357920196460544:\\
\;\;\;\;\frac{y - z}{t - z} \cdot x\\

\mathbf{elif}\;z \le 5.862038722875420925631635452195167558109 \cdot 10^{-249}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r13371988 = x;
        double r13371989 = y;
        double r13371990 = z;
        double r13371991 = r13371989 - r13371990;
        double r13371992 = r13371988 * r13371991;
        double r13371993 = t;
        double r13371994 = r13371993 - r13371990;
        double r13371995 = r13371992 / r13371994;
        return r13371995;
}
↓
double f(double x, double y, double z, double t) {
        double r13371996 = z;
        double r13371997 = -8.21599116430926e+38;
        bool r13371998 = r13371996 <= r13371997;
        double r13371999 = y;
        double r13372000 = r13371999 - r13371996;
        double r13372001 = t;
        double r13372002 = r13372001 - r13371996;
        double r13372003 = r13372000 / r13372002;
        double r13372004 = x;
        double r13372005 = r13372003 * r13372004;
        double r13372006 = 5.862038722875421e-249;
        bool r13372007 = r13371996 <= r13372006;
        double r13372008 = r13372004 * r13372000;
        double r13372009 = r13372008 / r13372002;
        double r13372010 = r13372007 ? r13372009 : r13372005;
        double r13372011 = r13371998 ? r13372005 : r13372010;
        return r13372011;
}

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

Original11.7
Target2.3
Herbie2.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.21599116430926e+38 or 5.862038722875421e-249 < z

    1. Initial program 14.7

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

    3. Applied *-un-lft-identity14.7

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

    if -8.21599116430926e+38 < z < 5.862038722875421e-249

    1. Initial program 5.1

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -821599116430925941436114357920196460544:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \mathbf{elif}\;z \le 5.862038722875420925631635452195167558109 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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