Average Error: 0.8 → 0.4
Time: 9.2s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.54279981406481496 \cdot 10^{213}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\\ \mathbf{elif}\;x \le 7.3933699298610861 \cdot 10^{209}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \end{array}\]
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 - z\right) \cdot \left(y - t\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r200963 = 1.0;
        double r200964 = x;
        double r200965 = y;
        double r200966 = z;
        double r200967 = r200965 - r200966;
        double r200968 = t;
        double r200969 = r200965 - r200968;
        double r200970 = r200967 * r200969;
        double r200971 = r200964 / r200970;
        double r200972 = r200963 - r200971;
        return r200972;
}
↓
double f(double x, double y, double z, double t) {
        double r200973 = x;
        double r200974 = -4.542799814064815e+213;
        bool r200975 = r200973 <= r200974;
        double r200976 = 1.0;
        double r200977 = 1.0;
        double r200978 = y;
        double r200979 = z;
        double r200980 = r200978 - r200979;
        double r200981 = r200977 / r200980;
        double r200982 = t;
        double r200983 = r200978 - r200982;
        double r200984 = r200981 / r200983;
        double r200985 = r200973 * r200984;
        double r200986 = r200976 - r200985;
        double r200987 = 7.393369929861086e+209;
        bool r200988 = r200973 <= r200987;
        double r200989 = r200973 / r200980;
        double r200990 = r200989 / r200983;
        double r200991 = r200976 - r200990;
        double r200992 = r200980 * r200983;
        double r200993 = r200973 / r200992;
        double r200994 = r200976 - r200993;
        double r200995 = r200988 ? r200991 : r200994;
        double r200996 = r200975 ? r200986 : r200995;
        return r200996;
}

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

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

  4. Final simplification0.4

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

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)))))