Average Error: 11.7 → 2.2
Time: 12.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r446279 = x;
        double r446280 = y;
        double r446281 = z;
        double r446282 = r446280 - r446281;
        double r446283 = r446279 * r446282;
        double r446284 = t;
        double r446285 = r446284 - r446281;
        double r446286 = r446283 / r446285;
        return r446286;
}
↓
double f(double x, double y, double z, double t) {
        double r446287 = z;
        double r446288 = -1.1536650006708072e-33;
        bool r446289 = r446287 <= r446288;
        double r446290 = -8.57064563000427e-270;
        bool r446291 = r446287 <= r446290;
        double r446292 = !r446291;
        bool r446293 = r446289 || r446292;
        double r446294 = x;
        double r446295 = y;
        double r446296 = r446295 - r446287;
        double r446297 = t;
        double r446298 = r446297 - r446287;
        double r446299 = r446296 / r446298;
        double r446300 = r446294 * r446299;
        double r446301 = r446294 / r446298;
        double r446302 = r446301 * r446296;
        double r446303 = r446293 ? r446300 : r446302;
        return r446303;
}

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
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1536650006708072e-33 or -8.57064563000427e-270 < z

    1. Initial program 13.2

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

    3. Applied *-un-lft-identity13.2

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -1.1536650006708072e-33 < z < -8.57064563000427e-270

    1. Initial program 5.3

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

    3. Applied associate-/l*5.2

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
    4. Using strategy rm

    5. Applied associate-/r/4.5

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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