Average Error: 11.9 → 2.4
Time: 7.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array}\]
\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}:\\
\;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r677547 = x;
        double r677548 = y;
        double r677549 = z;
        double r677550 = r677548 - r677549;
        double r677551 = r677547 * r677550;
        double r677552 = t;
        double r677553 = r677552 - r677549;
        double r677554 = r677551 / r677553;
        return r677554;
}
↓
double f(double x, double y, double z, double t) {
        double r677555 = z;
        double r677556 = -9.512737302380148e-222;
        bool r677557 = r677555 <= r677556;
        double r677558 = 5.4381737647266115e-107;
        bool r677559 = r677555 <= r677558;
        double r677560 = !r677559;
        bool r677561 = r677557 || r677560;
        double r677562 = x;
        double r677563 = y;
        double r677564 = r677563 - r677555;
        double r677565 = t;
        double r677566 = r677565 - r677555;
        double r677567 = r677564 / r677566;
        double r677568 = r677562 * r677567;
        double r677569 = r677562 / r677566;
        double r677570 = r677564 * r677569;
        double r677571 = r677561 ? r677568 : r677570;
        return r677571;
}

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 *-un-lft-identity6.7

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

    4. Applied times-frac5.5

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

    5. Simplified5.5

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

    7. Applied *-un-lft-identity5.5

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

    8. Applied associate-*l*5.5

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

    9. Simplified6.9

      \[\leadsto 1 \cdot \color{blue}{\left(\left(y - z\right) \cdot \frac{x}{t - z}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.4

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

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)))