Average Error: 7.5 → 2.2
Time: 7.1s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 6.34434390289444677 \cdot 10^{108}:\\ \;\;\;\;\frac{1}{\frac{y - z}{\frac{x}{t - z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 6.34434390289444677 \cdot 10^{108}:\\
\;\;\;\;\frac{1}{\frac{y - z}{\frac{x}{t - z}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r804616 = x;
        double r804617 = y;
        double r804618 = z;
        double r804619 = r804617 - r804618;
        double r804620 = t;
        double r804621 = r804620 - r804618;
        double r804622 = r804619 * r804621;
        double r804623 = r804616 / r804622;
        return r804623;
}
↓
double f(double x, double y, double z, double t) {
        double r804624 = y;
        double r804625 = z;
        double r804626 = r804624 - r804625;
        double r804627 = t;
        double r804628 = r804627 - r804625;
        double r804629 = r804626 * r804628;
        double r804630 = 6.344343902894447e+108;
        bool r804631 = r804629 <= r804630;
        double r804632 = 1.0;
        double r804633 = x;
        double r804634 = r804633 / r804628;
        double r804635 = r804626 / r804634;
        double r804636 = r804632 / r804635;
        double r804637 = r804633 / r804626;
        double r804638 = r804637 / r804628;
        double r804639 = r804631 ? r804636 : r804638;
        return r804639;
}

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

Target

Original7.5
Target8.2
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < 6.344343902894447e+108

    1. Initial program 5.2

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

    3. Applied *-un-lft-identity5.2

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

    4. Applied times-frac3.5

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

    6. Applied associate-*l/3.4

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

    7. Simplified3.4

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

    9. Applied *-un-lft-identity3.4

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

    10. Applied *-un-lft-identity3.4

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

    11. Applied times-frac3.4

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

    12. Applied associate-/l*3.8

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

    if 6.344343902894447e+108 < (* (- y z) (- t z))

    1. Initial program 9.8

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

    3. Applied associate-/r*0.5

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 6.34434390289444677 \cdot 10^{108}:\\ \;\;\;\;\frac{1}{\frac{y - z}{\frac{x}{t - z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))