Average Error: 0.8 → 0.4
Time: 7.1s
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 r286659 = 1.0;
        double r286660 = x;
        double r286661 = y;
        double r286662 = z;
        double r286663 = r286661 - r286662;
        double r286664 = t;
        double r286665 = r286661 - r286664;
        double r286666 = r286663 * r286665;
        double r286667 = r286660 / r286666;
        double r286668 = r286659 - r286667;
        return r286668;
}
↓
double f(double x, double y, double z, double t) {
        double r286669 = x;
        double r286670 = -4.542799814064815e+213;
        bool r286671 = r286669 <= r286670;
        double r286672 = 1.0;
        double r286673 = 1.0;
        double r286674 = y;
        double r286675 = z;
        double r286676 = r286674 - r286675;
        double r286677 = r286673 / r286676;
        double r286678 = t;
        double r286679 = r286674 - r286678;
        double r286680 = r286677 / r286679;
        double r286681 = r286669 * r286680;
        double r286682 = r286672 - r286681;
        double r286683 = 7.393369929861086e+209;
        bool r286684 = r286669 <= r286683;
        double r286685 = r286669 / r286676;
        double r286686 = r286685 / r286679;
        double r286687 = r286672 - r286686;
        double r286688 = r286679 * r286676;
        double r286689 = r286669 / r286688;
        double r286690 = r286672 - r286689;
        double r286691 = r286684 ? r286687 : r286690;
        double r286692 = r286671 ? r286682 : r286691;
        return r286692;
}

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 
(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)))))