Average Error: 7.1 → 1.6
Time: 17.8s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 2.671853008871483 \cdot 10^{-309}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;x \le 2.671853008871483 \cdot 10^{-309}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{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 ((x <= 2.671853008871483e-309)) {
		VAR = ((double) (((double) (x / ((double) (y - z)))) / ((double) (t - z))));
	} else {
		VAR = ((double) (((double) (((double) sqrt(x)) / ((double) (y - z)))) * ((double) (((double) sqrt(x)) / ((double) (t - 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

Original7.1
Target7.9
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2.671853008871483e-309

    1. Initial program 7.2

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

    3. Applied associate-/r*2.1

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

    if 2.671853008871483e-309 < x

    1. Initial program 6.9

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

    3. Applied add-sqr-sqrt7.1

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

    4. Applied times-frac1.0

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 2.671853008871483 \cdot 10^{-309}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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))))