Average Error: 11.9 → 2.4
Time: 3.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\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 r603227 = x;
        double r603228 = y;
        double r603229 = z;
        double r603230 = r603228 - r603229;
        double r603231 = r603227 * r603230;
        double r603232 = t;
        double r603233 = r603232 - r603229;
        double r603234 = r603231 / r603233;
        return r603234;
}
↓
double f(double x, double y, double z, double t) {
        double r603235 = z;
        double r603236 = -9.512737302380148e-222;
        bool r603237 = r603235 <= r603236;
        double r603238 = 5.4381737647266115e-107;
        bool r603239 = r603235 <= r603238;
        double r603240 = !r603239;
        bool r603241 = r603237 || r603240;
        double r603242 = x;
        double r603243 = y;
        double r603244 = r603243 - r603235;
        double r603245 = t;
        double r603246 = r603245 - r603235;
        double r603247 = r603244 / r603246;
        double r603248 = r603242 * r603247;
        double r603249 = r603242 / r603246;
        double r603250 = r603249 * r603244;
        double r603251 = r603241 ? r603248 : r603250;
        return r603251;
}

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

Original11.9
Target2.2
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.512737302380148e-222 or 5.4381737647266115e-107 < z

    1. Initial program 13.3

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

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

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

    4. Applied times-frac1.2

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

    5. Simplified1.2

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

    if -9.512737302380148e-222 < z < 5.4381737647266115e-107

    1. Initial program 6.7

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

    3. Applied associate-/l*5.6

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

    5. Applied associate-/r/6.9

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +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)))