Average Error: 11.7 → 2.5
Time: 15.9s
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 r31955326 = x;
        double r31955327 = y;
        double r31955328 = z;
        double r31955329 = r31955327 - r31955328;
        double r31955330 = r31955326 * r31955329;
        double r31955331 = t;
        double r31955332 = r31955331 - r31955328;
        double r31955333 = r31955330 / r31955332;
        return r31955333;
}
↓
double f(double x, double y, double z, double t) {
        double r31955334 = z;
        double r31955335 = -8.21599116430926e+38;
        bool r31955336 = r31955334 <= r31955335;
        double r31955337 = y;
        double r31955338 = r31955337 - r31955334;
        double r31955339 = t;
        double r31955340 = r31955339 - r31955334;
        double r31955341 = r31955338 / r31955340;
        double r31955342 = x;
        double r31955343 = r31955341 * r31955342;
        double r31955344 = 5.862038722875421e-249;
        bool r31955345 = r31955334 <= r31955344;
        double r31955346 = r31955342 * r31955338;
        double r31955347 = r31955346 / r31955340;
        double r31955348 = r31955345 ? r31955347 : r31955343;
        double r31955349 = r31955336 ? r31955343 : r31955348;
        return r31955349;
}

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)))