Average Error: 7.6 → 1.9
Time: 3.8s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -7.78744813119852 \cdot 10^{-180} \lor \neg \left(z \leq 2.4978070913607958 \cdot 10^{-195}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -7.78744813119852 \cdot 10^{-180} \lor \neg \left(z \leq 2.4978070913607958 \cdot 10^{-195}\right):\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.78744813119852e-180) (not (<= z 2.4978070913607958e-195)))
   (/ (/ x (- y z)) (- t z))
   (/ x (* (- y z) (- t z)))))
double code(double x, double y, double z, double t) {
	return (x / ((double) (((double) (y - z)) * ((double) (t - z)))));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z <= -7.78744813119852e-180) || !(z <= 2.4978070913607958e-195))) {
		tmp = ((x / ((double) (y - z))) / ((double) (t - z)));
	} else {
		tmp = (x / ((double) (((double) (y - z)) * ((double) (t - z)))));
	}
	return tmp;
}

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
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.7874481311985204e-180 or 2.4978070913607958e-195 < 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*_binary641.2

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

    if -7.7874481311985204e-180 < z < 2.4978070913607958e-195

    1. Initial program 5.7

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.78744813119852 \cdot 10^{-180} \lor \neg \left(z \leq 2.4978070913607958 \cdot 10^{-195}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))))