Average Error: 7.5 → 1.1
Time: 5.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -3.8613496221902048 \cdot 10^{167} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 4.10725892761908993 \cdot 10^{100}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -3.8613496221902048 \cdot 10^{167} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 4.10725892761908993 \cdot 10^{100}\right):\\
\;\;\;\;\frac{\frac{x}{y - z}}{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 r764276 = x;
        double r764277 = y;
        double r764278 = z;
        double r764279 = r764277 - r764278;
        double r764280 = t;
        double r764281 = r764280 - r764278;
        double r764282 = r764279 * r764281;
        double r764283 = r764276 / r764282;
        return r764283;
}
↓
double f(double x, double y, double z, double t) {
        double r764284 = y;
        double r764285 = z;
        double r764286 = r764284 - r764285;
        double r764287 = t;
        double r764288 = r764287 - r764285;
        double r764289 = r764286 * r764288;
        double r764290 = -3.861349622190205e+167;
        bool r764291 = r764289 <= r764290;
        double r764292 = 4.10725892761909e+100;
        bool r764293 = r764289 <= r764292;
        double r764294 = !r764293;
        bool r764295 = r764291 || r764294;
        double r764296 = x;
        double r764297 = r764296 / r764286;
        double r764298 = r764297 / r764288;
        double r764299 = r764296 / r764289;
        double r764300 = r764295 ? r764298 : r764299;
        return r764300;
}

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
Target8.3
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < -3.861349622190205e+167 or 4.10725892761909e+100 < (* (- y z) (- t z))

    1. Initial program 10.1

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

    3. Applied associate-/r*0.6

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

    if -3.861349622190205e+167 < (* (- y z) (- t z)) < 4.10725892761909e+100

    1. Initial program 2.0

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -3.8613496221902048 \cdot 10^{167} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 4.10725892761908993 \cdot 10^{100}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))))