Average Error: 11.6 → 2.2
Time: 2.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r615940 = x;
        double r615941 = y;
        double r615942 = z;
        double r615943 = r615941 - r615942;
        double r615944 = r615940 * r615943;
        double r615945 = t;
        double r615946 = r615945 - r615942;
        double r615947 = r615944 / r615946;
        return r615947;
}
↓
double f(double x, double y, double z, double t) {
        double r615948 = z;
        double r615949 = -3.543374415214875e-69;
        bool r615950 = r615948 <= r615949;
        double r615951 = 1.204072221446801e-212;
        bool r615952 = r615948 <= r615951;
        double r615953 = !r615952;
        bool r615954 = r615950 || r615953;
        double r615955 = x;
        double r615956 = t;
        double r615957 = r615956 - r615948;
        double r615958 = y;
        double r615959 = r615958 - r615948;
        double r615960 = r615957 / r615959;
        double r615961 = r615955 / r615960;
        double r615962 = r615959 * r615955;
        double r615963 = r615962 / r615957;
        double r615964 = r615954 ? r615961 : r615963;
        return r615964;
}

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

Original11.6
Target2.0
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.543374415214875e-69 or 1.204072221446801e-212 < z

    1. Initial program 13.4

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

    3. Applied associate-/l*1.0

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

    if -3.543374415214875e-69 < z < 1.204072221446801e-212

    1. Initial program 5.9

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

    3. Applied *-commutative5.9

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))