Average Error: 7.7 → 2.9
Time: 16.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 2.230776748510506 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;t \le 3.221537725138539 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;t \le 2.230776748510506 \cdot 10^{-184}:\\
\;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\

\mathbf{elif}\;t \le 3.221537725138539 \cdot 10^{+102}:\\
\;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r38646879 = x;
        double r38646880 = y;
        double r38646881 = z;
        double r38646882 = r38646880 - r38646881;
        double r38646883 = t;
        double r38646884 = r38646883 - r38646881;
        double r38646885 = r38646882 * r38646884;
        double r38646886 = r38646879 / r38646885;
        return r38646886;
}
↓
double f(double x, double y, double z, double t) {
        double r38646887 = t;
        double r38646888 = 2.230776748510506e-184;
        bool r38646889 = r38646887 <= r38646888;
        double r38646890 = x;
        double r38646891 = z;
        double r38646892 = r38646887 - r38646891;
        double r38646893 = r38646890 / r38646892;
        double r38646894 = y;
        double r38646895 = r38646894 - r38646891;
        double r38646896 = r38646893 / r38646895;
        double r38646897 = 3.221537725138539e+102;
        bool r38646898 = r38646887 <= r38646897;
        double r38646899 = r38646895 * r38646892;
        double r38646900 = r38646890 / r38646899;
        double r38646901 = r38646898 ? r38646900 : r38646896;
        double r38646902 = r38646889 ? r38646896 : r38646901;
        return r38646902;
}

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

Original7.7
Target8.4
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 2.230776748510506e-184 or 3.221537725138539e+102 < t

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.9

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)}\]

    4. Applied times-frac1.8

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
    5. Using strategy rm

    6. Applied associate-*l/2.6

      \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\sqrt[3]{x}}{t - z}}{y - z}}\]

    7. Simplified2.0

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

    if 2.230776748510506e-184 < t < 3.221537725138539e+102

    1. Initial program 5.5

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

    3. Applied add-cube-cbrt6.1

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)}\]

    4. Applied times-frac1.1

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
    5. Using strategy rm

    6. Applied associate-*l/2.2

      \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\sqrt[3]{x}}{t - z}}{y - z}}\]

    7. Simplified1.5

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

    9. Applied div-inv1.6

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

    10. Applied associate-/l*5.6

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

    11. Simplified5.5

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 2.230776748510506 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;t \le 3.221537725138539 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :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))))