Average Error: 7.8 → 0.9
Time: 4.9s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le -5.66814747540669434 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y - z}}{t - z}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 1.095105447 \cdot 10^{-316}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(y - z\right) \cdot \left(t - z\right)}{x}}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le -5.66814747540669434 \cdot 10^{-293}:\\
\;\;\;\;x \cdot \frac{\frac{1}{y - z}}{t - z}\\

\mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 1.095105447 \cdot 10^{-316}:\\
\;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\left(y - z\right) \cdot \left(t - z\right)}{x}}\\

\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) (x / ((double) (((double) (y - z)) * ((double) (t - z)))))) <= -5.668147475406694e-293)) {
		VAR = ((double) (x * ((double) (((double) (1.0 / ((double) (y - z)))) / ((double) (t - z))))));
	} else {
		double VAR_1;
		if ((((double) (x / ((double) (((double) (y - z)) * ((double) (t - z)))))) <= 1.0951054465953e-316)) {
			VAR_1 = ((double) (((double) (1.0 / ((double) (y - z)))) * ((double) (x / ((double) (t - z))))));
		} else {
			VAR_1 = ((double) (1.0 / ((double) (((double) (((double) (y - z)) * ((double) (t - z)))) / x))));
		}
		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

Original7.8
Target8.5
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ x (* (- y z) (- t z))) < -5.66814747540669434e-293

    1. Initial program 1.3

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

    3. Applied associate-/r*3.6

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

    5. Applied *-un-lft-identity3.6

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

    6. Applied div-inv3.7

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

    7. Applied times-frac1.6

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

    8. Simplified1.6

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

    if -5.66814747540669434e-293 < (/ x (* (- y z) (- t z))) < 1.095105447e-316

    1. Initial program 13.6

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

    3. Applied *-un-lft-identity13.6

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

    4. Applied times-frac0.2

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

    if 1.095105447e-316 < (/ x (* (- y z) (- t z)))

    1. Initial program 1.3

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

    3. Applied clear-num1.7

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le -5.66814747540669434 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y - z}}{t - z}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 1.095105447 \cdot 10^{-316}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(y - z\right) \cdot \left(t - z\right)}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020169 
(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))))