Average Error: 11.1 → 1.3
Time: 18.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r26185935 = x;
        double r26185936 = y;
        double r26185937 = z;
        double r26185938 = r26185936 - r26185937;
        double r26185939 = r26185935 * r26185938;
        double r26185940 = t;
        double r26185941 = r26185940 - r26185937;
        double r26185942 = r26185939 / r26185941;
        return r26185942;
}
↓
double f(double x, double y, double z, double t) {
        double r26185943 = y;
        double r26185944 = z;
        double r26185945 = r26185943 - r26185944;
        double r26185946 = x;
        double r26185947 = r26185945 * r26185946;
        double r26185948 = t;
        double r26185949 = r26185948 - r26185944;
        double r26185950 = r26185947 / r26185949;
        double r26185951 = 3.016949263831516e-301;
        bool r26185952 = r26185950 <= r26185951;
        double r26185953 = r26185949 / r26185945;
        double r26185954 = r26185946 / r26185953;
        double r26185955 = 5.367760633924734e+261;
        bool r26185956 = r26185950 <= r26185955;
        double r26185957 = r26185945 / r26185949;
        double r26185958 = r26185946 * r26185957;
        double r26185959 = r26185956 ? r26185950 : r26185958;
        double r26185960 = r26185952 ? r26185954 : r26185959;
        return r26185960;
}

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

Original11.1
Target2.1
Herbie1.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < 3.016949263831516e-301

    1. Initial program 10.9

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

    3. Applied associate-/l*1.9

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

    if 3.016949263831516e-301 < (/ (* x (- y z)) (- t z)) < 5.367760633924734e+261

    1. Initial program 0.3

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

    if 5.367760633924734e+261 < (/ (* x (- y z)) (- t z))

    1. Initial program 53.2

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

    3. Applied *-un-lft-identity53.2

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +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)))