Average Error: 0.8 → 0.4
Time: 3.2s
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 r215138 = 1.0;
        double r215139 = x;
        double r215140 = y;
        double r215141 = z;
        double r215142 = r215140 - r215141;
        double r215143 = t;
        double r215144 = r215140 - r215143;
        double r215145 = r215142 * r215144;
        double r215146 = r215139 / r215145;
        double r215147 = r215138 - r215146;
        return r215147;
}
↓
double f(double x, double y, double z, double t) {
        double r215148 = x;
        double r215149 = -4.542799814064815e+213;
        bool r215150 = r215148 <= r215149;
        double r215151 = 1.0;
        double r215152 = 1.0;
        double r215153 = y;
        double r215154 = z;
        double r215155 = r215153 - r215154;
        double r215156 = r215152 / r215155;
        double r215157 = t;
        double r215158 = r215153 - r215157;
        double r215159 = r215156 / r215158;
        double r215160 = r215148 * r215159;
        double r215161 = r215151 - r215160;
        double r215162 = 7.393369929861086e+209;
        bool r215163 = r215148 <= r215162;
        double r215164 = r215148 / r215155;
        double r215165 = r215164 / r215158;
        double r215166 = r215151 - r215165;
        double r215167 = r215155 * r215158;
        double r215168 = r215148 / r215167;
        double r215169 = r215151 - r215168;
        double r215170 = r215163 ? r215166 : r215169;
        double r215171 = r215150 ? r215161 : r215170;
        return r215171;
}

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 
(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)))))