Average Error: 7.6 → 1.3
Time: 4.2s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.42138227223074828 \cdot 10^{248}:\\ \;\;\;\;\frac{x \cdot \frac{1}{y - z}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le -6.7089921577106081 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \end{array}\]
\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 -2.42138227223074828 \cdot 10^{248}:\\
\;\;\;\;\frac{x \cdot \frac{1}{y - z}}{t - z}\\

\mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le -6.7089921577106081 \cdot 10^{-293}:\\
\;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x / ((double) (((double) (y - z)) * ((double) (t - z))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (y - z)) * ((double) (t - z)))) <= -2.4213822722307483e+248)) {
		VAR = ((double) (((double) (x * ((double) (1.0 / ((double) (y - z)))))) / ((double) (t - z))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y - z)) * ((double) (t - z)))) <= -6.708992157710608e-293)) {
			VAR_1 = ((double) (x * ((double) (1.0 / ((double) (((double) (y - z)) * ((double) (t - z))))))));
		} else {
			VAR_1 = ((double) (((double) (1.0 / ((double) (((double) (y - z)) / x)))) / ((double) (t - z))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original7.6
Target8.2
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- y z) (- t z)) < -2.4213822722307483e+248

    1. Initial program 16.1

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

    3. Applied associate-/r*0.1

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

    5. Applied div-inv0.2

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

    if -2.4213822722307483e+248 < (* (- y z) (- t z)) < -6.708992157710608e-293

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

    if -6.708992157710608e-293 < (* (- y z) (- t z))

    1. Initial program 8.0

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

    3. Applied associate-/r*1.7

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

    5. Applied clear-num1.8

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{y - z}{x}}}}{t - z}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.42138227223074828 \cdot 10^{248}:\\ \;\;\;\;\frac{x \cdot \frac{1}{y - z}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le -6.7089921577106081 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020122 +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))))