Average Error: 11.5 → 2.2
Time: 4.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.462290720716170268145851842092576515123 \cdot 10^{-19} \lor \neg \left(z \le 6.646211365845630643018977419410525880821 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.462290720716170268145851842092576515123 \cdot 10^{-19} \lor \neg \left(z \le 6.646211365845630643018977419410525880821 \cdot 10^{-98}\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r586095 = x;
        double r586096 = y;
        double r586097 = z;
        double r586098 = r586096 - r586097;
        double r586099 = r586095 * r586098;
        double r586100 = t;
        double r586101 = r586100 - r586097;
        double r586102 = r586099 / r586101;
        return r586102;
}
↓
double f(double x, double y, double z, double t) {
        double r586103 = z;
        double r586104 = -2.4622907207161703e-19;
        bool r586105 = r586103 <= r586104;
        double r586106 = 6.64621136584563e-98;
        bool r586107 = r586103 <= r586106;
        double r586108 = !r586107;
        bool r586109 = r586105 || r586108;
        double r586110 = x;
        double r586111 = t;
        double r586112 = r586111 - r586103;
        double r586113 = y;
        double r586114 = r586113 - r586103;
        double r586115 = r586112 / r586114;
        double r586116 = r586110 / r586115;
        double r586117 = r586110 * r586113;
        double r586118 = -r586103;
        double r586119 = r586110 * r586118;
        double r586120 = r586117 + r586119;
        double r586121 = r586120 / r586112;
        double r586122 = r586109 ? r586116 : r586121;
        return r586122;
}

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

Original11.5
Target2.1
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.4622907207161703e-19 or 6.64621136584563e-98 < z

    1. Initial program 15.3

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

    3. Applied associate-/l*0.3

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

    if -2.4622907207161703e-19 < z < 6.64621136584563e-98

    1. Initial program 5.3

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

    3. Applied sub-neg5.3

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

    4. Applied distribute-lft-in5.3

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.462290720716170268145851842092576515123 \cdot 10^{-19} \lor \neg \left(z \le 6.646211365845630643018977419410525880821 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 +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)))