Average Error: 11.8 → 1.5
Time: 14.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.426882217422760647491241614519693519843 \cdot 10^{-216}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{1}{y - z} \cdot \left(t - z\right)}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty:\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.426882217422760647491241614519693519843 \cdot 10^{-216}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r22788828 = x;
        double r22788829 = y;
        double r22788830 = z;
        double r22788831 = r22788829 - r22788830;
        double r22788832 = r22788828 * r22788831;
        double r22788833 = t;
        double r22788834 = r22788833 - r22788830;
        double r22788835 = r22788832 / r22788834;
        return r22788835;
}
↓
double f(double x, double y, double z, double t) {
        double r22788836 = y;
        double r22788837 = z;
        double r22788838 = r22788836 - r22788837;
        double r22788839 = x;
        double r22788840 = r22788838 * r22788839;
        double r22788841 = t;
        double r22788842 = r22788841 - r22788837;
        double r22788843 = r22788840 / r22788842;
        double r22788844 = -inf.0;
        bool r22788845 = r22788843 <= r22788844;
        double r22788846 = r22788838 / r22788842;
        double r22788847 = r22788839 * r22788846;
        double r22788848 = -1.4268822174227606e-216;
        bool r22788849 = r22788843 <= r22788848;
        double r22788850 = 1.0;
        double r22788851 = r22788850 / r22788838;
        double r22788852 = r22788851 * r22788842;
        double r22788853 = r22788839 / r22788852;
        double r22788854 = r22788849 ? r22788843 : r22788853;
        double r22788855 = r22788845 ? r22788847 : r22788854;
        return r22788855;
}

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

Original11.8
Target2.3
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -inf.0 < (/ (* x (- y z)) (- t z)) < -1.4268822174227606e-216

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac3.1

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

    5. Simplified3.1

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

    7. Applied associate-*r/0.3

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

    if -1.4268822174227606e-216 < (/ (* x (- y z)) (- t z))

    1. Initial program 10.0

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

    3. Applied associate-/l*2.2

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

    5. Applied div-inv2.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.426882217422760647491241614519693519843 \cdot 10^{-216}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{1}{y - z} \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 +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)))