Average Error: 7.6 → 1.6
Time: 3.1s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le -1.22042495711387302 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 7.9176643066215467 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array}\]
\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 -1.22042495711387302 \cdot 10^{-264}:\\
\;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\

\mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 7.9176643066215467 \cdot 10^{-227}:\\
\;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{t - z}}{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) (x / ((double) (((double) (y - z)) * ((double) (t - z)))))) <= -1.220424957113873e-264)) {
		VAR = ((double) (x / ((double) (((double) (y - z)) * ((double) (t - z))))));
	} else {
		double VAR_1;
		if ((((double) (x / ((double) (((double) (y - z)) * ((double) (t - z)))))) <= 7.917664306621547e-227)) {
			VAR_1 = ((double) (((double) (x / ((double) (y - z)))) * ((double) (1.0 / ((double) (t - z))))));
		} else {
			VAR_1 = ((double) (((double) (x / ((double) (t - z)))) / ((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
Target8.4
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 3 regimes

  2. if (/ x (* (- y z) (- t z))) < -1.22042495711387302e-264

    1. Initial program 1.7

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

    if -1.22042495711387302e-264 < (/ x (* (- y z) (- t z))) < 7.9176643066215467e-227

    1. Initial program 12.2

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

    3. Applied *-un-lft-identity12.2

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

    4. Applied times-frac0.9

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

    6. Applied div-inv0.9

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

    7. Applied associate-*r*0.9

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

    8. Simplified0.8

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

    if 7.9176643066215467e-227 < (/ x (* (- y z) (- t z)))

    1. Initial program 1.6

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

    3. Applied *-un-lft-identity1.6

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

    4. Applied times-frac3.7

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

    6. Applied associate-*l/3.6

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

    7. Simplified3.6

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le -1.22042495711387302 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \le 7.9176643066215467 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array}\]

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))))