Average Error: 11.9 → 2.4
Time: 6.6s
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 r724060 = x;
        double r724061 = y;
        double r724062 = z;
        double r724063 = r724061 - r724062;
        double r724064 = r724060 * r724063;
        double r724065 = t;
        double r724066 = r724065 - r724062;
        double r724067 = r724064 / r724066;
        return r724067;
}
↓
double f(double x, double y, double z, double t) {
        double r724068 = z;
        double r724069 = -9.512737302380148e-222;
        bool r724070 = r724068 <= r724069;
        double r724071 = 5.4381737647266115e-107;
        bool r724072 = r724068 <= r724071;
        double r724073 = !r724072;
        bool r724074 = r724070 || r724073;
        double r724075 = x;
        double r724076 = y;
        double r724077 = r724076 - r724068;
        double r724078 = t;
        double r724079 = r724078 - r724068;
        double r724080 = r724077 / r724079;
        double r724081 = r724075 * r724080;
        double r724082 = r724075 / r724079;
        double r724083 = r724082 * r724077;
        double r724084 = r724074 ? r724081 : r724083;
        return r724084;
}

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)))