Average Error: 7.7 → 2.9
Time: 17.3s
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 r36728507 = x;
        double r36728508 = y;
        double r36728509 = z;
        double r36728510 = r36728508 - r36728509;
        double r36728511 = t;
        double r36728512 = r36728511 - r36728509;
        double r36728513 = r36728510 * r36728512;
        double r36728514 = r36728507 / r36728513;
        return r36728514;
}
↓
double f(double x, double y, double z, double t) {
        double r36728515 = t;
        double r36728516 = 2.230776748510506e-184;
        bool r36728517 = r36728515 <= r36728516;
        double r36728518 = x;
        double r36728519 = z;
        double r36728520 = r36728515 - r36728519;
        double r36728521 = r36728518 / r36728520;
        double r36728522 = y;
        double r36728523 = r36728522 - r36728519;
        double r36728524 = r36728521 / r36728523;
        double r36728525 = 3.221537725138539e+102;
        bool r36728526 = r36728515 <= r36728525;
        double r36728527 = r36728523 * r36728520;
        double r36728528 = r36728518 / r36728527;
        double r36728529 = r36728526 ? r36728528 : r36728524;
        double r36728530 = r36728517 ? r36728524 : r36728529;
        return r36728530;
}

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))))