Average Error: 7.0 → 1.5
Time: 15.8s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 0.0:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 0.0:\\
\;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r527392 = x;
        double r527393 = y;
        double r527394 = z;
        double r527395 = r527393 - r527394;
        double r527396 = t;
        double r527397 = r527396 - r527394;
        double r527398 = r527395 * r527397;
        double r527399 = r527392 / r527398;
        return r527399;
}
↓
double f(double x, double y, double z, double t) {
        double r527400 = x;
        double r527401 = y;
        double r527402 = z;
        double r527403 = r527401 - r527402;
        double r527404 = t;
        double r527405 = r527404 - r527402;
        double r527406 = r527403 * r527405;
        double r527407 = r527400 / r527406;
        double r527408 = 0.0;
        bool r527409 = r527407 <= r527408;
        double r527410 = 1.0;
        double r527411 = r527403 / r527400;
        double r527412 = r527410 / r527411;
        double r527413 = r527412 / r527405;
        double r527414 = r527409 ? r527413 : r527407;
        return r527414;
}

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

Original7.0
Target7.8
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x (* (- y z) (- t z))) < 0.0

    1. Initial program 7.2

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

    3. Applied associate-/r*2.1

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

    5. Applied clear-num2.2

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

    if 0.0 < (/ x (* (- y z) (- t z)))

    1. Initial program 6.8

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 0.0:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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))))