Average Error: 7.6 → 1.2
Time: 4.1s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 2.3409123974934257 \cdot 10^{-222}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 4.8221499848062026 \cdot 10^{227}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{t - z}{x}}}{y - z}\\ \end{array}\]
\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 2.3409123974934257 \cdot 10^{-222}:\\
\;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\

\mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 4.8221499848062026 \cdot 10^{227}:\\
\;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{\frac{t - z}{x}}}{y - 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)))) <= 2.3409123974934257e-222)) {
		VAR = ((double) (((double) (1.0 / ((double) (y - z)))) * ((double) (x / ((double) (t - z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y - z)) * ((double) (t - z)))) <= 4.8221499848062026e+227)) {
			VAR_1 = ((double) (x * ((double) (1.0 / ((double) (((double) (y - z)) * ((double) (t - z))))))));
		} else {
			VAR_1 = ((double) (((double) (1.0 / ((double) (((double) (t - z)) / x)))) / ((double) (y - 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
Target8.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- y z) (- t z)) < 2.3409123974934257e-222

    1. Initial program 7.9

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

    3. Applied *-un-lft-identity7.9

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

    4. Applied times-frac2.9

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

    if 2.3409123974934257e-222 < (* (- y z) (- t z)) < 4.8221499848062026e227

    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 4.8221499848062026e227 < (* (- y z) (- t z))

    1. Initial program 12.7

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

    3. Applied add-cube-cbrt12.8

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)}\]

    4. Applied times-frac0.4

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
    5. Using strategy rm

    6. Applied associate-*l/0.5

      \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\sqrt[3]{x}}{t - z}}{y - z}}\]

    7. Simplified0.1

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

    9. Applied clear-num0.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 2.3409123974934257 \cdot 10^{-222}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 4.8221499848062026 \cdot 10^{227}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{t - z}{x}}}{y - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))))