Average Error: 11.7 → 2.5
Time: 14.8s
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 r22234441 = x;
        double r22234442 = y;
        double r22234443 = z;
        double r22234444 = r22234442 - r22234443;
        double r22234445 = r22234441 * r22234444;
        double r22234446 = t;
        double r22234447 = r22234446 - r22234443;
        double r22234448 = r22234445 / r22234447;
        return r22234448;
}
↓
double f(double x, double y, double z, double t) {
        double r22234449 = z;
        double r22234450 = -8.21599116430926e+38;
        bool r22234451 = r22234449 <= r22234450;
        double r22234452 = y;
        double r22234453 = r22234452 - r22234449;
        double r22234454 = t;
        double r22234455 = r22234454 - r22234449;
        double r22234456 = r22234453 / r22234455;
        double r22234457 = x;
        double r22234458 = r22234456 * r22234457;
        double r22234459 = 5.862038722875421e-249;
        bool r22234460 = r22234449 <= r22234459;
        double r22234461 = r22234457 * r22234453;
        double r22234462 = r22234461 / r22234455;
        double r22234463 = r22234460 ? r22234462 : r22234458;
        double r22234464 = r22234451 ? r22234458 : r22234463;
        return r22234464;
}

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 +o rules:numerics
(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)))