Average Error: 11.7 → 2.3
Time: 4.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 1.369752526671511722658526908528908232804 \cdot 10^{-295} \lor \neg \left(z \le 1.627532321675118910729324718829559319672 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t - z}{x \cdot \left(y - z\right)}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le 1.369752526671511722658526908528908232804 \cdot 10^{-295} \lor \neg \left(z \le 1.627532321675118910729324718829559319672 \cdot 10^{-108}\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{t - z}{x \cdot \left(y - z\right)}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r658702 = x;
        double r658703 = y;
        double r658704 = z;
        double r658705 = r658703 - r658704;
        double r658706 = r658702 * r658705;
        double r658707 = t;
        double r658708 = r658707 - r658704;
        double r658709 = r658706 / r658708;
        return r658709;
}
↓
double f(double x, double y, double z, double t) {
        double r658710 = z;
        double r658711 = 1.3697525266715117e-295;
        bool r658712 = r658710 <= r658711;
        double r658713 = 1.627532321675119e-108;
        bool r658714 = r658710 <= r658713;
        double r658715 = !r658714;
        bool r658716 = r658712 || r658715;
        double r658717 = x;
        double r658718 = t;
        double r658719 = r658718 - r658710;
        double r658720 = y;
        double r658721 = r658720 - r658710;
        double r658722 = r658719 / r658721;
        double r658723 = r658717 / r658722;
        double r658724 = 1.0;
        double r658725 = r658717 * r658721;
        double r658726 = r658719 / r658725;
        double r658727 = r658724 / r658726;
        double r658728 = r658716 ? r658723 : r658727;
        return r658728;
}

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
Target2.4
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 1.3697525266715117e-295 or 1.627532321675119e-108 < z

    1. Initial program 12.6

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

    3. Applied associate-/l*1.7

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

    5. Applied div-inv1.9

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

    7. Applied un-div-inv1.7

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

    if 1.3697525266715117e-295 < z < 1.627532321675119e-108

    1. Initial program 5.6

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

    3. Applied clear-num5.9

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 1.369752526671511722658526908528908232804 \cdot 10^{-295} \lor \neg \left(z \le 1.627532321675118910729324718829559319672 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t - z}{x \cdot \left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 +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)))