Average Error: 11.5 → 2.2
Time: 4.2s
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 r673944 = x;
        double r673945 = y;
        double r673946 = z;
        double r673947 = r673945 - r673946;
        double r673948 = r673944 * r673947;
        double r673949 = t;
        double r673950 = r673949 - r673946;
        double r673951 = r673948 / r673950;
        return r673951;
}
↓
double f(double x, double y, double z, double t) {
        double r673952 = z;
        double r673953 = -2.4622907207161703e-19;
        bool r673954 = r673952 <= r673953;
        double r673955 = 6.64621136584563e-98;
        bool r673956 = r673952 <= r673955;
        double r673957 = !r673956;
        bool r673958 = r673954 || r673957;
        double r673959 = x;
        double r673960 = t;
        double r673961 = r673960 - r673952;
        double r673962 = y;
        double r673963 = r673962 - r673952;
        double r673964 = r673961 / r673963;
        double r673965 = r673959 / r673964;
        double r673966 = r673959 * r673962;
        double r673967 = -r673952;
        double r673968 = r673959 * r673967;
        double r673969 = r673966 + r673968;
        double r673970 = r673969 / r673961;
        double r673971 = r673958 ? r673965 : r673970;
        return r673971;
}

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 
(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)))