Average Error: 0.8 → 0.4
Time: 8.2s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.54279981406481496 \cdot 10^{213}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\\ \mathbf{elif}\;x \le 7.3933699298610861 \cdot 10^{209}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\\ \end{array}\]
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 r389633 = 1.0;
        double r389634 = x;
        double r389635 = y;
        double r389636 = z;
        double r389637 = r389635 - r389636;
        double r389638 = t;
        double r389639 = r389635 - r389638;
        double r389640 = r389637 * r389639;
        double r389641 = r389634 / r389640;
        double r389642 = r389633 - r389641;
        return r389642;
}
↓
double f(double x, double y, double z, double t) {
        double r389643 = x;
        double r389644 = -4.542799814064815e+213;
        bool r389645 = r389643 <= r389644;
        double r389646 = 1.0;
        double r389647 = 1.0;
        double r389648 = y;
        double r389649 = z;
        double r389650 = r389648 - r389649;
        double r389651 = r389647 / r389650;
        double r389652 = t;
        double r389653 = r389648 - r389652;
        double r389654 = r389651 / r389653;
        double r389655 = r389643 * r389654;
        double r389656 = r389646 - r389655;
        double r389657 = 7.393369929861086e+209;
        bool r389658 = r389643 <= r389657;
        double r389659 = r389643 / r389650;
        double r389660 = r389659 / r389653;
        double r389661 = r389646 - r389660;
        double r389662 = r389653 * r389650;
        double r389663 = r389643 / r389662;
        double r389664 = r389646 - r389663;
        double r389665 = r389658 ? r389661 : r389664;
        double r389666 = r389645 ? r389656 : r389665;
        return r389666;
}

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)))))