Average Error: 7.3 → 0.7
Time: 3.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) = -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 2.37517183699055636 \cdot 10^{168}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]
\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) = -\infty:\\
\;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\

\mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 2.37517183699055636 \cdot 10^{168}:\\
\;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\end{array}
double code(double x, double y, double z, double t) {
	return (x / ((y - z) * (t - z)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((y - z) * (t - z)) <= -inf.0)) {
		VAR = ((x / (t - z)) / (y - z));
	} else {
		double VAR_1;
		if ((((y - z) * (t - z)) <= 2.3751718369905564e+168)) {
			VAR_1 = (x / ((t - z) * (y - z)));
		} else {
			VAR_1 = ((x / (y - z)) / (t - 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

Original7.3
Target8.2
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- y z) (- t z)) < -inf.0

    1. Initial program 21.5

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

    3. Applied *-commutative21.5

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

    4. Applied associate-/r*0.1

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

    if -inf.0 < (* (- y z) (- t z)) < 2.3751718369905564e+168

    1. Initial program 1.3

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

    3. Applied *-commutative1.3

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

    if 2.3751718369905564e+168 < (* (- y z) (- t z))

    1. Initial program 10.6

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

    3. Applied associate-/r*0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) = -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 2.37517183699055636 \cdot 10^{168}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(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 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))