Average Error: 7.8 → 0.7
Time: 17.1s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) = -\infty \lor \neg \left(\left(t - z\right) \cdot \left(y - z\right) \le 1.217220199270374023216280482755360574816 \cdot 10^{303}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) = -\infty \lor \neg \left(\left(t - z\right) \cdot \left(y - z\right) \le 1.217220199270374023216280482755360574816 \cdot 10^{303}\right):\\
\;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r475371 = x;
        double r475372 = y;
        double r475373 = z;
        double r475374 = r475372 - r475373;
        double r475375 = t;
        double r475376 = r475375 - r475373;
        double r475377 = r475374 * r475376;
        double r475378 = r475371 / r475377;
        return r475378;
}
↓
double f(double x, double y, double z, double t) {
        double r475379 = t;
        double r475380 = z;
        double r475381 = r475379 - r475380;
        double r475382 = y;
        double r475383 = r475382 - r475380;
        double r475384 = r475381 * r475383;
        double r475385 = -inf.0;
        bool r475386 = r475384 <= r475385;
        double r475387 = 1.217220199270374e+303;
        bool r475388 = r475384 <= r475387;
        double r475389 = !r475388;
        bool r475390 = r475386 || r475389;
        double r475391 = x;
        double r475392 = r475391 / r475381;
        double r475393 = r475392 / r475383;
        double r475394 = r475391 / r475384;
        double r475395 = r475390 ? r475393 : r475394;
        return r475395;
}

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

Original7.8
Target8.7
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < -inf.0 or 1.217220199270374e+303 < (* (- y z) (- t z))

    1. Initial program 17.3

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

    3. Applied *-un-lft-identity17.3

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

    4. Applied times-frac0.1

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

    6. Applied associate-*l/0.1

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

    7. Simplified0.1

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

    if -inf.0 < (* (- y z) (- t z)) < 1.217220199270374e+303

    1. Initial program 1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) = -\infty \lor \neg \left(\left(t - z\right) \cdot \left(y - z\right) \le 1.217220199270374023216280482755360574816 \cdot 10^{303}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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 (/ 1.0 (* (- y z) (- t z)))))

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