Average Error: 0.8 → 0.4
Time: 8.0s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.54279981406481496 \cdot 10^{213}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\\ \mathbf{elif}\;x \le 7.3933699298610861 \cdot 10^{209}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\\ \end{array}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.54279981406481496 \cdot 10^{213}:\\
\;\;\;\;1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\\

\mathbf{elif}\;x \le 7.3933699298610861 \cdot 10^{209}:\\
\;\;\;\;1 - \frac{\frac{x}{y - z}}{y - t}\\

\mathbf{else}:\\
\;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r244955 = 1.0;
        double r244956 = x;
        double r244957 = y;
        double r244958 = z;
        double r244959 = r244957 - r244958;
        double r244960 = t;
        double r244961 = r244957 - r244960;
        double r244962 = r244959 * r244961;
        double r244963 = r244956 / r244962;
        double r244964 = r244955 - r244963;
        return r244964;
}
↓
double f(double x, double y, double z, double t) {
        double r244965 = x;
        double r244966 = -4.542799814064815e+213;
        bool r244967 = r244965 <= r244966;
        double r244968 = 1.0;
        double r244969 = 1.0;
        double r244970 = y;
        double r244971 = z;
        double r244972 = r244970 - r244971;
        double r244973 = r244969 / r244972;
        double r244974 = t;
        double r244975 = r244970 - r244974;
        double r244976 = r244973 / r244975;
        double r244977 = r244965 * r244976;
        double r244978 = r244968 - r244977;
        double r244979 = 7.393369929861086e+209;
        bool r244980 = r244965 <= r244979;
        double r244981 = r244965 / r244972;
        double r244982 = r244981 / r244975;
        double r244983 = r244968 - r244982;
        double r244984 = r244975 * r244972;
        double r244985 = r244965 / r244984;
        double r244986 = r244968 - r244985;
        double r244987 = r244980 ? r244983 : r244986;
        double r244988 = r244967 ? r244978 : r244987;
        return r244988;
}

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

Derivation

  1. Split input into 3 regimes

  2. if x < -4.542799814064815e+213

    1. Initial program 0.2

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
    2. Using strategy rm

    3. Applied associate-/r*5.8

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity5.8

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

    6. Applied div-inv5.9

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

    7. Applied times-frac0.2

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

    8. Simplified0.2

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

    if -4.542799814064815e+213 < x < 7.393369929861086e+209

    1. Initial program 0.9

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
    2. Using strategy rm

    3. Applied associate-/r*0.4

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

    if 7.393369929861086e+209 < x

    1. Initial program 0.2

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
    2. Using strategy rm

    3. Applied associate-/r*4.5

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}}\]
    4. Using strategy rm

    5. Applied div-inv4.5

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

    6. Applied associate-/l*0.2

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

    7. Simplified0.2

      \[\leadsto 1 - \frac{x}{\color{blue}{\left(y - t\right) \cdot \left(y - z\right)}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.54279981406481496 \cdot 10^{213}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\\ \mathbf{elif}\;x \le 7.3933699298610861 \cdot 10^{209}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1 (/ x (* (- y z) (- y t)))))