Average Error: 11.4 → 1.3
Time: 14.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0:\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r26394219 = x;
        double r26394220 = y;
        double r26394221 = z;
        double r26394222 = r26394220 - r26394221;
        double r26394223 = r26394219 * r26394222;
        double r26394224 = t;
        double r26394225 = r26394224 - r26394221;
        double r26394226 = r26394223 / r26394225;
        return r26394226;
}
↓
double f(double x, double y, double z, double t) {
        double r26394227 = y;
        double r26394228 = z;
        double r26394229 = r26394227 - r26394228;
        double r26394230 = x;
        double r26394231 = r26394229 * r26394230;
        double r26394232 = t;
        double r26394233 = r26394232 - r26394228;
        double r26394234 = r26394231 / r26394233;
        double r26394235 = -0.0;
        bool r26394236 = r26394234 <= r26394235;
        double r26394237 = r26394229 / r26394233;
        double r26394238 = r26394230 * r26394237;
        double r26394239 = 4.4211586881981104e+222;
        bool r26394240 = r26394234 <= r26394239;
        double r26394241 = r26394240 ? r26394234 : r26394238;
        double r26394242 = r26394236 ? r26394238 : r26394241;
        return r26394242;
}

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

Original11.4
Target2.1
Herbie1.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) (- t z)) < -0.0 or 4.4211586881981104e+222 < (/ (* x (- y z)) (- t z))

    1. Initial program 17.4

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

    3. Applied *-un-lft-identity17.4

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

    if -0.0 < (/ (* x (- y z)) (- t z)) < 4.4211586881981104e+222

    1. Initial program 0.3

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +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)))