Average Error: 11.6 → 2.2
Time: 7.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(-z\right) \cdot x}{t - z}\\ \end{array}\]
\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{y \cdot x + \left(-z\right) \cdot x}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r733172 = x;
        double r733173 = y;
        double r733174 = z;
        double r733175 = r733173 - r733174;
        double r733176 = r733172 * r733175;
        double r733177 = t;
        double r733178 = r733177 - r733174;
        double r733179 = r733176 / r733178;
        return r733179;
}
↓
double f(double x, double y, double z, double t) {
        double r733180 = z;
        double r733181 = -3.543374415214875e-69;
        bool r733182 = r733180 <= r733181;
        double r733183 = 1.204072221446801e-212;
        bool r733184 = r733180 <= r733183;
        double r733185 = !r733184;
        bool r733186 = r733182 || r733185;
        double r733187 = x;
        double r733188 = t;
        double r733189 = r733188 - r733180;
        double r733190 = y;
        double r733191 = r733190 - r733180;
        double r733192 = r733189 / r733191;
        double r733193 = r733187 / r733192;
        double r733194 = r733190 * r733187;
        double r733195 = -r733180;
        double r733196 = r733195 * r733187;
        double r733197 = r733194 + r733196;
        double r733198 = r733197 / r733189;
        double r733199 = r733186 ? r733193 : r733198;
        return r733199;
}

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 sub-neg5.9

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

    4. Applied distribute-lft-in5.9

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

    5. Simplified5.9

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

    6. Simplified5.9

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

  4. Final simplification2.2

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

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)))