Average Error: 7.5 → 2.2
Time: 4.0s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.68384852863096308 \cdot 10^{-258} \lor \neg \left(z \le 9.19688633809727201 \cdot 10^{-261}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.68384852863096308 \cdot 10^{-258} \lor \neg \left(z \le 9.19688633809727201 \cdot 10^{-261}\right):\\
\;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\

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

\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 (((z <= -7.683848528630963e-258) || !(z <= 9.196886338097272e-261))) {
		VAR = ((double) (((double) (x / ((double) (t - z)))) / ((double) (y - z))));
	} else {
		VAR = ((double) (x / ((double) (((double) (t - z)) * ((double) (y - z))))));
	}
	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

Original7.5
Target8.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.68384852863096308e-258 or 9.19688633809727201e-261 < z

    1. Initial program 7.6

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

    3. Applied *-un-lft-identity7.6

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

    4. Applied times-frac1.9

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

    6. Applied associate-*l/1.9

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

    7. Simplified1.9

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

    if -7.68384852863096308e-258 < z < 9.19688633809727201e-261

    1. Initial program 5.9

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.68384852863096308 \cdot 10^{-258} \lor \neg \left(z \le 9.19688633809727201 \cdot 10^{-261}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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 (/ 1.0 (* (- y z) (- t z)))))

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